MOTION SAMPLE BOOKLET CLASS IX MOTION MATTER IN OUR SURROUNDINGS FUNDAMENTAL UNIT NUMBER SYSTEM THE FRENCH REVOLUTION

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1 MOTION SAMPLE BOOKLET CLASS IX MOTION MATTER IN OUR SURROUNDINGS FUNDAMENTAL UNIT NUMBER SYSTEM THE FRENCH REVOLUTION

2 Copyright reserved with Motion Edu. Pvt. Ltd. nd Publictions All rights reserved. No prt of this work herein should be reproduced or used either grphiclly, electroniclly, mechniclly or by recording, photocopying, tping, web distributing or by storing in ny form nd retrieving without the prior written permission of the publisher. Anybody violting this is lible to be leglly prosecuted. Corporte Hed Office 94 - Rjeev Gndhi Ngr Kot, (Rj.) Ph. No. : , IVRS No : ,,, www. motioniitjee.com, info@motioniitjee.com

3 THEORY AND EXERCISE BOOKLET CONTENTS MOTION CLASS - IX S.NO. TOPIC PAGE NO. THEORY... 4 SOLVED EXAMPLE... EXERCISE - I... EXERCISE -II MATTER IN OUR SURROUNDINGS S.NO. TOPIC PAGE NO. THEORY SOLVED EXAMPLE EXERCISE - I EXERCISE -II FUNDAMENTAL UNIT S.NO. TOPIC PAGE NO. THEORY SOLVED EXAMPLE EXERCISE - I EXERCISE -II

4 THEORY AND EXERCISE BOOKLET CONTENTS NUMBER SYSTEM S.NO. TOPIC PAGE NO. THEORY SOLVED EXAMPLE EXERCISE - I EXERCISE -II... EXERCISE -III... THE FRENCH REVOLUTION S.NO. TOPIC PAGE NO. THEORY... 8 EXERCISE - I EXERCISE -II... 0

5 MOTION Pge # CONTENTS IN THE CHAPTER INTRODUCTION TYPES OF MOTION DISTANCE & DISPLACEMENT SPEED AND VELOCITY ACCELERATION EQUATIONS OF MOTION DERIVATION OF EQUATIONS OF MOTION EQUATIONS OF MOTION GRAPHICAL METHOD BODY FALLING FREELY UNDER GRAVITY BODY IS PROJECTED VERTICALLY UP DISPLACEMENT- TIME GRAPH VELOCITY -TIME GRAPH ACCELERATION TIME GRAPH CIRCULAR MOTION PROJECTILE MOTION : , url : : info@motioniitjee.com

6 Pge # 6 MOTION INTRODUCTION Motion is very preliminry stte of ction ssocited with living nd non-living beings. The study of the displcement, velocity nd ccelertion ssocited with moving bodies cn mke us understnd the motion of bodies. To hve n in-depth study of motion, equtionl representtion nd grphicl nlysis of vrious relted quntities in motion with time is lso done. When body does not chnge its position with time, we cn sy tht the body is t rest. While if body chnges its position with time, it is sid to be in motion. (i) An object is sid to be point object if it chnges its position by distnces which re much greter thn its size. (ii) A point or some sttionry object with respect to which body continuously chnges its position in the stte of motion is known s origin or reference point. Describing Motion : When tree, is observed by n observer A sitting on bench, the tree is t rest. This is becuse position of the tree is not chnging with respect to the observer A. Now, When the sme tree T is observed by n observer sitting in superfst trin moving with velocity v, then the tree is moving with respect to the observer becuse the position of tree is chnging with respect to the observer B. Vectors : Physicl quntities defined with both mgnitude nd direction re clled vector quntities. They should lso stisfy the lw of vector ddition. Exmples: Velocity, ccelertion, force, displcement, momentum, weight, torque, electric field, mgnetic filed, etc. Sclrs : Physicl quntities hving only mgnitude re clled sclr quntities. Exmples: Mss, time, distnce, speed, work, power, energy, electric chrge, re, volume, density, pressure, electric potentil, temperture, etc. DIFFERENCE BETWEEN SCALAR & VECTOR QUANTITIES : Sclr Quntities These re completely specified by their mgnitude only. These chnge by chnge of their mgnitude only These re dded or subtrcted by lws of ordinry lgebr like 4m+m=9m. Vector quntities These re completely specified by their mgnitude s well s direction. These chnge by chnge of either their mgnitude or direction or both These re dded or subtrcted by lws of vector ddition. Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

7 MOTION Pge # 7 Newton's Thought Discuss whether the wlls of your clssroom re t rest or in motion. Explntion The wlls of our clssroom re t rest with respect to the ground or erth. But, they re in motion with respect to n object or n observer outside the erth. This is becuse the erth is moving bout its own xis s well s it is revolving round the sun. Thus, the stte of rest nd motion re not bsolute, they re reltive terms. TYPES OF MOTION (A) According to Directions (i) One dimensionl motion is the motion of prticle moving long stright line. (ii) Two dimensionl motion A prticle moving long curved pth in plne hs -dimensionl motion. (iii) Three dimensionl motion Prticle moving in spce hs -dimensionl motion. (B) According to stte of motion A moving body my cover equl distnces in equl intervls of time or different distnces in equl intervls of time. On the bsis of bove ssumption, the motion of body cn be clssified s uniform motion nd non-uniform motion. (i) Uniform motion: Time (in second) Distnce covered (in metre) When body covers equl distnces in equl intervls of time however smll my be time intervls, the body is sid to describe uniform motion. Exmple of uniform motion () An eroplne flying t speed of 600 km/h Time (b) A trin running t speed of 0 km/h (c) Light energy trvelling t speed of 0 8 m/s (d) A spceship moving t speed of 00 km/s (ii) Non-uniform motion: Time (in second) Distnce (in metre) Time When body covers unequl distnces in equl intervls of time, the body is sid to be moving with non-uniform motion. : , url : : info@motioniitjee.com

8 Pge # 8 MOTION Exmple of non-uniform motion (C) (i) An eroplne running on runwy before tking off. (ii) A freely flling stone under the ction of grvity. (iii) An object thrown verticlly upwrd. (iv)when the brkes re pplied to moving cr. According to pth (i) Liner motion : A body hs liner motion if it moves in stright line or pth. Ex. () Motion of moving cr on stright rod. (b) Motion of bll dropped from the roof of building. (ii) Circulr (or rottionl) Motion : A body hs circulr motion if it moves round fixed point. A verticl pssing through the fixed point round which the body moves is known s xis of rottion. Ex. () Motion of n electric fn. (b) Motion of merry-go-round (c) Motion of spinning top. Object Axis of rottion (iii) Vibrtory motion : A body hs vibrtory motion if it moves to nd fro bout fixed point. Ex. () Motion of pendulum of wll clock. (b) Motion of simple pendulum. Bob DISTANCE & DISPLACEMENT (i) The ctul pth length between the initil nd finl positions of the prticle gives the distnce covered by the prticle. (ii) The minimum distnce between the initil nd finl positions of body during tht time intervl is clled displcement. Anlysis (i) Distnce trvelled is sclr quntity while displcement is vector quntity. Eg. if body moves long the circumference of circle of rdius r, then the distnce trvelled is given by r, while the displcement is given by zero. (ii) When body continuously moves in the sme stright line nd in the sme direction then displcement will be equl to the distnce trvelled. But if the body chnges its direction while moving, then the displcement is smller thn the distnce trvelled. Displcement Distnce A I C II r A B Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

9 MOTION Pge # 9 DIFFERENC ES BETWEEN DISTANCE AND DISPLAC EMENT Distnce It is defined s the c tul pth trversed by body. Displcement It is the shortest distnce between two points whic h the body moves. It is sclr quntity It is vec tor quntity It c n never be negtive or zero It c n be negtive, zero or positive. 4 Distnc e c n be equl to or greter thn displc ement Displc ement c n be equl to or less thn distnc e. Distnc e trvelled is not unique pth between two points. Displc ement is unique pth between two points. 6 7 T he distnce between two points gives full informtion of the type of pth followed by the body. Distnc e never dec reses with time. for moving body it is never zero. Displc ement between two points does not give full informtion of the type of pth followed by the body. Displc ement c n decrese with time for moving body it c nbe zero. 8 Distnc e in SI is mesured in metre Displc ement in SI is mesured in metre. A honeybee leves the hive nd trvels m before returning. Is the displcement for the trip the sme s the distnce trvelled? If not, why not. Hive Newton's Thought Honey bee Explntion No, the displcement nd the distnce re not sme. This is becuse the displcement is the chnge of position of object in motion while distnce is length of pth trvelled by it. Here, the distnce trvelled = m While, the displcement = 0, becuse the position of honey bee is not chnged. SPEED AND VELOCITY Speed : The distnce trvelled in one second is clled speed It is sclr quntity. Its SI unit is m/s. Speed lwys remins positive. Distnce Speed (m / s) Time Speed s s s t t t Where s = distnce in time intervl t. : , url : : info@motioniitjee.com

10 Pge # 0 MOTION Velocity : The displcement in one second is clled velocity. It is vector quntity expressed in m/s. Velocity cn be positive, negtive or zero. Displcement Velocity (ms ) Time tken Velo city s t Where s = displcement trvelled in time intervl t. Speed. Sclr quntity. Rte of distnce covered.. Cnnot be zero for moving body. 4. Speed is velocity without direction.. Speed in SI unit is mesured in ms -. Velocity. Vector quntity.. Rte of displcement.. Cn be zero, +ve or ve. 4. Velocity is directed speed.. Velocity in SI unit is mesured in ms -. (i) Unit : In M.K.S. system = ms In C.G.S. system = Cms (ii) If distnce time grph is stright line, then speed cn be given by the slope of the line, s i.e. v = t slope = s t s t (iii) The re of velocity time grph gives distnce trvelled. (iv) Conversion from km/hr to m/sec. s t t s km hr = m/s = 8 m/s. TYPES OF SPEED () Averge nd Instntneous speed Averge speed : The rtio of distnce trvelled by body to the totl time tken, when the motion cn be with vrying speeds for vrious intervls of time. Averge Speed Totl Distnce Totl Time tken OR It is obtined by dividing the totl distnce trvelled by the totl time intervl. i.e. Averge speed s s s t t t Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

11 MOTION Pge # (i) Averge speed is sclr, while verge velocity is vector. (ii) For given time intervl verge velocity is single mny vlues depending on pth following. (iii) If fter motion body comes bck to its initil position nd finite (s s > 0) vlued, while verge speed cn hve v v = 0 [s r = 0], but v v > 0 (iv) For moving body verge speed cn never be ve or zero (unless t = 0), while verge velocity cn be i.e. v v > 0 while v v > = or < 0 (v) In generl verge speed is not equl to mgnitude of verge velocity (s s ¹ r ). However it cn be so if the motion is long stright line without chnge in direction (s s = r ) (vi) If prticle trvels distnces L, L L t speeds v, v, v etc respectively, then v v = s t = L L v L L v Ln L n v n = Li Li vi (vii) If prticle trvels t speeds v, v etc for intervls t, t etc respectively, then vt vt... vit i v v = t t... = ti (viii) If prticle moves distnce t speed v nd comes bck with speed v, then vv verge speed v v = v v ( v v = 0) (ix) If prticle moves for two equl time intervls v v = v v Instntneous speed : The speed of body t prticulr instnt of time is clled its instntneous speed. s ds Ins tn tn eous speed lim t 0 t dt Time(t) (b) Uniform nd Non uniform speed Uniform speed : If the time speed grph of n object is stright line prllel to time xis then the body is moving with uniform speed. Non-uniform speed : If the speed of body is chnging with respect to time it is moving with non-uniform speed. Its grph is not stright line. : , url : : info@motioniitjee.com

12 Pge # MOTION TYPES OF VELOCITY () Averge Velocity: Totl displcement divided by totl time is clled n verge velocity. Totl displcement Averge velocity Totl time tken x x Vv t t OR The rithmetic men of initil velocity nd finl velocity for given time period, is clled verge velocity. Averge velocity V v u v Initil velocity + Finl velocity (b) where u = initil velocity, v = finl velocity Uniform & Non uniform Velocity Uniform velocity A B C D m m m s s s motion Body moving with uniform velocity When body covers equl displcement in equl intervl of time, the body is sid to be moving with uniform velocity. Non-uniform velocity/vrible velocity : A B C D m m 7m s s s motion Body moving with non-uniform velocity When body covers unequl displcement in equl intervls of time, the body is sid to be moving with vrible velocity. Instntneous velocity : The velocity of body t prticulr instnt of time is clled its instntneous velocity. Time(t) r dr Ins tntneous velocity lim t 0 t dt Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

13 MOTION Pge # Newton's Thought A prticle is thrown verticlly upwrds under grvity. Wht re the signs of displcement nd velocity in the given situtions () & (b) (P to Q): Explntion () Here, displcement nd velocity (verge & instntneous) both re positive. (b)here, displcement is positive. Instntneous velocity is negtive & verge velocity is positive. Q P () P (b) Q ACCELERATION The rte t which the velocity chnges is clled ccelertion. It is vector quntity. Its SI unit is m/s or ms. (i) Rte of chnge of velocity is clled ccelertion (ii) The chnge in velocity my be in mgnitude or in direction or both. v u i.e. t (iii) Unit of ccelertion = m/s or ms Decelertion or Retrdtion : If the chnge in velocity is ve ie. if velocity of body decreses, the ccelertion is clled decelertion or retrdtion. Uniformly ccelerted motion : When the chnge in velocity is sme in equl time intervls, the motion clled uniformly ccelerted motion, otherwise, it is non-uniformly ccelerted motion. TYPES OF ACCELERATION (i) (ii) Uniform & Non uniform ccelertion Uniform ccelertion If body trvels in stright line nd its velocity increses by equl mounts in equl intervls of time then it is sid to be in stte of uniform ccelertion e.g. motion of freely flling body. Non uniform ccelertion A body hs non-uniform ccelertion if its velocity increses by unequl mounts in equl intervls of time. Averge & Instntneous ccelertion Averge ccelertion : v v v v t t t [here it is ssumed tht ccelertion remins the sme during the time intervl Dt.] If body trvels with uniform ccelertion for time intervl t nd with uniform ccelertion for time intervl t then v (t t ) (t t ) Instntneous ccelertion : The ccelertion of body t ny instnt is clled its instntneous ccelertion. : , url : : info@motioniitjee.com

14 Pge # 4 MOTION v Time(t) e.g. = lim t 0 v t = dv dt (iii) If the velocity of body decreses, then it will experience negtive ccelertion which is clled decelertion or retrdtion. Accelertion is determined by the slope of time-velocity grph. tn dv dt (i) If the time velocity grph is stright line, ccelertion remins constnts. (ii) If the slope of the stright line is positive, positive ccelertion occurs. (iii) If the slope of the stright line is negtive, negtive ccelertion or retrdtion occurs. (iv) Lrger the slope (tn ) longer will be the stright line. (v) If the time velocity grph is curve, then the ccelertion chnges continuously. EQUATIONS OF MOTION A. Uniform Motion : If x i nd x f re the initil nd finl positions respectively of -moving prticle, the motion is defined by, velocity v x f xi nd v will be constnt. t B. Non-uniform Motion : (x f x i ) vries in equl time intervls. So velocity vries. C. Averge velocity = D. Averge speed = Totl displcement Totl time tken Totl distnce trvelled Totl time tken E. Uniform ccelertion : If u nd v re the initil nd finl velocities in time 't', then ccelertion v u. It is constnt. t F. In uniform ccelertion (only), the verge velocity is given by, v v = G. For uniformly ccelerted motion, (i) v = u + t (ii) s = ut + t nd (iii) v = u + s v u. Motion under uniform ccelertion Suppose body strts with initil velocity u, moving with n ccelertion ttins velocity v fter time t trvels distnce s, then motion cn be described by following equtions. () v = u + t (b) s = ut + t (c) v = u + s Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

15 MOTION Pge # Newton's Thought A cr is trvelling long stright rod nd is decelerting. Does the cr's ccelertion necessrily hve negtive vlue? Explntion We begin with the mening of the term "decelerting," which hs nothing to do with whether the ccelertion '' is positive or negtive. The term mens only tht the ccelertion is opposite to the velocity nd indictes tht the moving object is slowing down. (i) One possibility is tht the velocity of the cr points to the right (the positive direction) nd ccelertion points opposite i.e. to the left (the negtive direction). (ii) Another possibility is tht the velocity of the cr points to the left (the negtive direction) nd ccelertion points opposite i.e. to the right (the positive direction). DERIVATION OF EQUATIONS OF MOTION v v v = ve; = +ve v = +ve; = ve (i) v = u + t Let body hve n initil velocity 'u' nd n uniform ccelertion ''. At ny time 't', if 'v' is the velocity, Accelertion = v = u + t Chnge in velocity Time tken v u t (ii) s = ut + t Let the displcement in time 't' be 's' with uniform ccelertion ''. The verge velocity is given by v v initilvelocity finl velocity v v = u v Displcement s u v t Applying first eq. s u u t t ; s = (u t) t s = ut + t. (iii) v = u + s Velocity t ny time, v = u + t s = u v t s = v u v u v = u + s v u t v u t : , url : : info@motioniitjee.com

16 Pge # 6 MOTION (A) (B) (C) It my be remembered lwys tht these equtions re pplicble only for constnt ccelertion or Uniform Accelertion. The equtions of motion under grvity cn be obtined by replcing ccelertion by ccelertion due to grvity (g) nd cn be written s follows : When the body is coming towrds the centre of erth () v = u + gt ; (b) h = ut + gt ; (c) v = u + gh (D) When body is thrown upwrds with some initil velocity, then retrdtion produced due to ttrction of the erth. In equtions of motion, is replced by ( g) nd thus equtions become. () v = u gt ; (b) h = ut gt ; (c) v = u gh (E) Distnce covered by body in n th sec. i.e. s n = u + (n ) Newton's Thought An object moving with constnt ccelertion cn certinly slow down. But cn n object ever come to permnent hlt (stop) if its ccelertion truly remins constnt? Explin. Explntion An object moving with constnt ccelertion will slow down if the ccelertion is opposite to the velocity. However, if the ccelertion remins constnt the object will never come to permnent hlt. As time increse, the mgnitude of the velocity will get smller nd smller. At some time, the velocity will be instntneously zero. An instnt fter the velocity is zero, the mgnitude of the velocity will begin incresing in the sme direction s the ccelertion. As time increses, the velocity of the object will then increse in the sme direction s the ccelertion. In other words, if the ccelertion truly remins constnt, the object will slow down, stop for n instnt, reverse direction nd then speed up. Point of reversl u- Velocity decreses v = 0 Velocity increses Constnt ccelertion cting on object BODY FALLING FREELY UNDER GRAVITY A body relesed ner the surfce of the erth is ccelerted downwrd under the influence of force of grvity. () Time of Flight : from eqution S = ut + t S = H, u = 0, = g t = T (Let ssume) H = (0)T gt T = H g Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.) H (0,0) u=0

17 MOTION Pge # 7 (b) Finl Velocity when body reches the ground from v u = s s = H v = v f u = 0 = g v f 0 = ( g) ( H) v f = gh Assuming u = 0 for freely flling body : (i) As h = gt i.e. h t Distnce fllen in time t, t, t etc will be in the rtio of : :... i.e. squre of integers. (ii) The distnce fllen in n th sec = g(n ) so distnce fllen in I st, nd, rd sec will be in the rtio : : i.e. odd integers only. (i) (ii) It includes two types of motion BODY IS PROJECTED VERTICALLY UP Decelerted motion from A to B becuse the direction of velocity nd ccelertion is opposite. So speed decreses Accelerted motion from B to C becuse the direction of velocity nd ccelertion is sme (downwrd). So speed increses () Time of flight : upwrd motion (deccelerted motion) u downwrd motion (ccelerted motion) It is the time tken by the prticle to rech the ground. If the prticle is thrown verticlly upwrd with initil velocity u then u i = u from eqution = g (tke downwrd direction negtive) S = ut + t S net = 0 (when prticle gin reches the ground) t = T (time of flight) 0 = ut gt (b) Mximum Height : from v u + s T = u g t mximum height v = 0, s = H mx (c) Finl velocity 0 = u gh mx H mx = u g from v = u + t v = v f = g t = T = u g v f = u v f = u g i.e. the body reches the ground with the sme speed with which it ws thrown verticlly upwrds s it thrown verticlly upwrd. Tking initil position s origin nd direction of motion (i.e. verticlly up) s positive. () At the highest point v = 0 (b) = g : , url : : info@motioniitjee.com u g A B C

18 Pge # 8 MOTION It is cler tht in cse of motion under grvity () Time tken to go up is equl to the time tken to fll down through the sme distnce. (b) The speed with which body is projected up is equl to the speed with which it comes bck to the point of projection. (c) The body returns to the strting point with the sme speed with which it ws thrown. DISPLACEMENT- TIME GRAPH The slope of displcement time (x t) grph gives the velocity of motion. One cn find the velocity of motion, finding the slope of x - t grph. To find the slope, (i) Select ny two points on the grph A nd B. (ii) Drw right tringle below the grph (ABT) (iii) Find the length of BT nd AT from the xis x B (iv) Tke the rtio of BT to AT The rtio hs the units of velocity. A T Slope BT AT Displcement Time tken Velocity t If x-t grph is stright line, then there my be (i) Stte of rest prllel to time xis (ii) uniform motion inclined to time xis. The slope of the stright line is mesure of velocity of motion. If the x t grph is not stright line, the motion will be non-uniform motion ccelerted motion. For exmple, body dropped from height undergoes free fll stisfying the reltion y = Displcement- time grph (exmples) x gt. () x 0 Body is t rest t x 0. t x () Body strts from origin nd is moving with speed tn wy from origin. x t () Body strts from rest from origin nd moves wy from origin with incresing speed velocity nd positive ccelertion. t Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

19 (4) MOTION x Pge # 9 Body strts from rest from x = x 0 nd moves wy from origin with incresing velocity or +ve ccelertion. x 0 t () x 0 Body strts from x = x 0 nd is moving towrd the origin with constnt velocity psses throw origin fter sme time nd continues to move wy from origin. t x (6) x 0 Body strts from rest t x = x 0 nd then moves with incresing speed towrds origin ccelertion is ve t (7) x Body strts moving wy from origin with some initil speed. Speed of body is decresing till t nd it becomes 0 momentrily of t = t nd At this instnt. Its reverses its direction nd move towrds the origin with incresing speed. O t t t (8) x t t t Body strts from origin moves wy from origin in the ve x-xis t t = t with decresing speed nd t t= t it comes t rest momentrily, Reverses its direction moves towrds the origin the incresing speed. Crosses the origin t t = t. x (9) t Body strts from origin from rest nd moves wy from origin with incresing speed. VELOCITY -TIME GRAPH The slope of velocity-time (v t) grph gives the ccelertion of motion. v B Slope of v t grph is, BT AT Chnge in velocity Time tken A T If v t grph is stright line, then there my be (i) uniform motion prllel to time xis t (ii) non-uniform motion inclined to time xis. : , url : : info@motioniitjee.com

20 Pge # 0 MOTION Velocity -time grph (exmples) v () Body is lwys t rest. t v () v 0 Body is moving with constnt velocity v 0 t v () Body is t rest initilly then it strts moving with its velocity incresing t constnt rte i.e. body is moving with constnt ccelertion. t v (4) v 0 Body strts its motion with initil velocity v 0 nd continues to move with its velocity incresing t constnt rte i.e. ccelertion of the body is constnt. t () v v 0 v t0 t Body strts its motion with initil velocity v 0. Then it continues to move with its velocity decresing t constnt rte i.e. ccelertion of the body is negtive nd constnt. At t = t 0 the body comes to rest instntneously nd reverses its direction of motion nd then continues to move with decresing velocity or incresing speed. For 0 < t < t 0 motion of the body is decelerted ( speed is decresing) t > t 0 motion of the body is ccelerted ( speed is incresing) (6) t Body is t rest initilly. Then it strts moving with incresing velocity. As time increses its velocity is incresing more rpidly. i.e. the moving with incresing ccelertion. (7) v v 0 t 0 t Body strts its motion with initil velocity v 0. Its velocity is decresing with time nd t t = t 0. It becomes zero fter body reverse its direction of motion nd continues to move with decresing velocity or incresing speed. Since velocity of the body is decresing for whole motion. Therefore, its ccelertion is negtive.for 0 < t < t 0 motion of the body is decelerted (speed is decresing) t > t 0 motion of the body is ccelerted ( speed is incresing) Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

21 () MOTION ACCELERATION TIME GRAPH Pge # ccelertion of the body is zero tht mens the body is moving constnt velocity. t () t Accelertion of the body is constnt nd positive. () t Accelertion of the body is constnt nd negtive (4) t Initilly the ccelertion of the body is zero. Then its ccelertion is incresing t constnt rte. () t The body strts ccelerting(initil ccelertion zero) t t = 0. Its ccelertion is negtive for whole of its motion nd is decresing t constnt rte. (6) t Nture of Slope:- y y Initilly ccelertion of the body is zero. Its ccelertion is positive for whole of its motion. Its ccelertion is incresing for whole of its motion. Slope = 0 x COMPETITIVE WINDOW y Slope incresing x Slope = +ve y x y Slope decresing x Slope = ve y x y Slope constnt Slope incresing x Slope = x : , url : : info@motioniitjee.com

22 Pge # MOTION Newton's Thought Two crs moving on stright sections of highwy. The ccelertion of the first cr A is greter thn the ccelertion of the second cr B nd both ccelertions hve the sme direction. Which one of the following is true? () The velocity of the first cr is lwys greter thn the velocity of the second cr. (b) The velocity of the second cr is lwys greter thn the velocity of the first cr. (c) In the sme time intervl, the velocity of the first cr chnges by greter mount thn the velocity of the second cr does. (d) In the sme time intervl, the velocity of the second cr chnges by greter mount thn the velocity of the first cr does. Explntion Option (c) is true becuse the ccelertion of the first cr is greter thn the ccelertion of the second cr, thus in the sme time intervl, the velocity of the first cr chnges by greter mount tht the velocity of the second cr does. Option (d) is reverse of option (c), thus it cnnot be true simultneously. It is therefore, flse sttement. Option () is flse becuse initil velocity of cr A my be less thn the velocity of cr B. After certin time intervl, velocity of A will become more thn the velocity of B. Option (b) is lso flse becuse initil velocity of cr A my be less or more thn the velocity of cr B. Even if the initil velocity of cr B is more thn velocity of cr A, fter certin time intervl it will become less thn tht of cr A. EQUATIONS OF MOTION GRAPHICAL METHOD I. Velocity-time eqution Consider the v t grph shown for body hving velocity u t t = 0 nd v t t seconds. The ccelertion '' ssocited with the motion is given by, slope BC AB v t u 0 v u t v u = t or v = u + t v(ms ) v C II. Position-time eqution : Are below the v t grph is mesure of the displcement in stright line. Displcement s = Are (OACBD) s = (BC OD) + OA OD = t t + ut ( v u = t) u A O B D (s) t s =ut + t III. Position-velocity equtions : Displcement in 't' seconds is given by s = Are of trpezium OACBD = (OA + CD) OD = (u + v) t s = (u + v) v u = v u v u = s v = u + s Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

23 MOTION Pge # CIRCULAR MOTION Motion in circulr pth is clled circulr motion. It is of two kinds uniform or non- uniform. If the speed of motion is sme in the circulr pth, the motion is clled uniform circulr motion. If the speed vries my increse or decrese, then it is non-uniform circulr motion. In circulr motion of rdius r, (i) Angulr displcement = rc length rdius x r (ii) Angulr velocity = f t i (iii) Liner velocity v = rdius ngulr velocity v = r (iv) Angulr ccelertion f t i (v) Liner ccelertion = rdius ngulr ccelertion (v) Liner ccelertion = r UNIFORM CIRCULAR MOTION : (i) If the rdius vector sweeps out equl ngles in equl times, then its motion is sid to be uniform circulr motion. (ii) In uniform circulr motion speed remins const. (iii) Liner velocity, being vector quntity, its direction chnges continuously. (iv)the direction of velocity is long the tngent t every point. Angulr displcement : : , url : : info@motioniitjee.com O P' s r P In circulr motion, the ngle subtended t the centre by ny rc of the circulr pth of motion is clled the ngulr displcement ( ). It is mesured in rdins. One rdin is tht ngulr displcement whose re length is equl to the rdius of the circle. Angulr velocity : The ngulr displcement of ny moving object per second is clled its ngulr velocity ( ). Angulr velocity ( ) = Angulr displceme nt Time tken It is expressed in rdin per second. (i) A vector quntity (ii) Direction is perpendiculr to plne of rottion t. Note : If the prticle is revolving in the clockwise direction then the direction of ngulr velocity is perpendiculr to the plne downwrds. Wheres in cse of nticlockwise direction the direction will be upwrds. (iii) Unit is Rdin/sec. (iv) In uniform circulr motion the direction of ngulr velocity is long the xis of rottion which is constnt throughout. (v) Angulr velocity remins constnt in mgnitude s well s in direction. (vi) v = r where r = rdius of the circle.

24 Pge # 4 MOTION Angulr ccelertion : The chnge in ngulr velocity in unit time is clled the ngulr ccelertion ( ). Angulr ccelertion = Chnge in ngulr velocity Time tken (i) Accelertion in uniform circulr motion is directed towrds the centre nd the direction of velocity t ny instnt is given by the tngent t tht point. (ii) Since the ccelertion is lwys directed towrds the centre in uniform circulr motion, it is n exmple of vrible ccelertion even through the mgnitude of ccelertion is the sme. Centripetl ccelertion : (i) In uniform circulr motion the prticle experiences n ccelertion clled the centripetl ccelertion. v (ii) c r (iii) The direction of centripetl ccelertion is long the rdius towrds the centre. Centripetl force : (i) Alwys cts towrds centre. (ii) Centripetl force is required to move prticle in circle. (iii) Becuse F c is lwys perpendiculr to velocity or displcement, hence the work done by this force will lwys be zero. Note : (i) Circulr motion in horizontl plne is usully uniform circulr motion. (ii) Remember tht equtions of motion re not pplicble for circulr motion. Time period : (i) It is the time tken to complete one complete revolution. (ii) In one revolution, ngle subtended is nd if T is time period, then the ngulr velocity is given by T Frequency : or T (i) Frequency is defined s the no. of revolutions per second. i.e. n T DO YOU KNOW? If on X-xis & on Y-xis then Slope Formul Time Displcement Velocity v ds sf si vv dt time Time Velocity Accelertion dv vf vi v dt time Time Momentum Force F dp W Pv dt time Time Energy Power P dw dt v J f J i time Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

25 MOTION Pge # SOLVED PROBLEMS Ex. Sol. An object hs moved through distnce. Cn it hve zero displcement? If yes, support you nswer with n exmple. Yes, n object which hs moved through distnce cn hve zero displcement. Exmple : When person, wlking long circulr pth, returns bck to the strting point, fter completing circle, his displcement is zero. But he covers distnce r where 'r' is the rdius of circulr pth. The displcement is zero, s the shortest distnce between the initil nd finl position of the person is zero. Ex. A frmer moves long the boundry of squre field of side 0 m in 40 s. Wht will be the mgnitude of displcement of the frmer t the end of minutes 0 seconds? Sol. The perimeter squre field ABCD = 4 0m = 40 m. Time for moving round the 0 m squre field once = 40 s. Time for journey of frmer = min nd 0 s = 40 s. A D Number of times the frmer moves round the squre field = times. 0 m For going once round the squre field, the displcement = 0 For going thrice round the squre field, the displcement = 0 B C 0 m For going times the squre field, the distnce covered = 40 m = 0 m. It is obvious from the figure, tht if the frmer strts from pt A, then he will cover 0 m long AB nd then0 m long BC. Therefore displcement of frmer from the point A to point C is AC (AB) (BC) (0) (0) 4.4 m Ex. Which of the following is true for displcement? () It cnnot be zero. (b) Its mgnitude is greter thn the distnce trvelled by the object. Sol. None of the sttement () or (b) is true for displcement. Ex.4 Sol. Ex. Sol. Distinguish between speed nd velocity. (i) Speed is the rte of chnge of motion but velocity is the rte of chnge of motion in specified direction. (ii) Speed is sclr quntity, but velocity is vector quntity. Under wht condition is the mgnitude of verge velocity of n object equl to its verge speed? The mgnitude of verge velocity of n object is equl to its verge speed when the velocity of n object chnges t uniform rte, i.e., the body is in uniformly ccelerted motion. If body is moving with uniform ccelertion. Initil velocity = u, Finl velocity = v, Averge speed = Averge velocity = u v. SPEED Speed of body is the distnce trvelled by the body per unit time. or The rte of chnge of motion is clled speed. distnce trvelled Speed = time tken If body covers distnce S in time t then speed, v S t : , url : : info@motioniitjee.com

26 Pge # 6 MOTION Ex.6 Wht does speedometer of n utomobile mesure? Sol. The speedometer mesures the instntneous speed of the utomobile t some prticulr time. Ex.7 Wht does the pth of n object look like when it is in uniform motion? Sol. The pth of n object will be stright line. Ex.8 During n experiment, signl from spceship reched the ground sttion in five minutes. Wht ws the distnce of the spceship from the ground sttion? The signl trvels t the speed of light, tht is 0 8 ms. Sol. Speed of signl = 0 8 ms Time in which signl reches ground = min = 60 = 00 s Distnce of spceship from the ground level = speed time = = m Ex.9 Sol. When will you sy body is in (i) Uniform ccelertion. (ii) Non uniform ccelertion? (i) A body is in uniform ccelertion when equl chnges in velocity tke plce in equl intervls of time,however smll these intervls my be. (ii) A body is sid to be possessing non-uniform ccelertion when unequl chnges in velocity tke plce in equl intervls of time, however smll these intervls my be. Ex.0 A bus decreses its speed from 80 km h to 60 km h in s. Find the ccelertion of the bus. Sol. Given t = s Initil speed of bus u = 80 km h = 80 8 Finl speed of the bus v = 60 km h = 60 8 =. ms = 6.7 ms Now ccelertion is given by the reltion v u 6.7. t. ms - Ex. A trin strting from rilwy sttion nd moving with uniform ccelertion ttins speed 40 kmh in 0 minutes. Find its ccelertion. Sol. Given t = 0 min = 0 60 = 600 s Initil speed of trin, u = 0 ms Finl speed of trin v = 40 km h = 40 8 =. ms Now ccelertion is given by the reltion v u. 0 t ms - Ex. Wht is the nture of the distnce time grphs for uniform nd non-uniform motion of n object? Sol. The distnce time-grph for uniform motion is stright line not prllel to the time xis. The distnce time-grph for non-uniform motion is not stright line. It cn be curve or zigzg line not prllel to time xis. Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

27 MOTION Pge # 7 Ex. Wht cn you sy bout the motion of n object whose distnce time-grph is stright line prllel to the time xis? Sol. The object is sttionry. Ex.4 Wht cn you sy bout the motion of n object if its speed-time grph is stright line prllel to the time xis? Sol. The object hs uniform speed. Ex. Wht is the quntity which is mesured by the re occupied below the velocity-time grph? Sol. Displcement is the quntity which is mesured by the re under velocity time grph. Ex.6 A bus strting from rest moves with uniform ccelertion of 0. ms for minutes. Find () the speed cquired. (b) the distnce trvelled. Sol. Given Initil speed of bus, u = 0 ms Finl speed of bus, v =? = 0. ms, t = min = 0 s S =? (i) We know, v = u + t or v = = ms (ii) S = ut + t S = (0) = 70 m Therefore Finl speed cquired = ms Distnce trvelled = 70 m Ex.7 A trin is trvelling t speed of 90 kmh. Brkes re pplied so s to produce uniform ccelertion of 0. ms. Find how fr the trin will go before it is brought to rest. Sol. Given Initil speed of trin, u = 90 km h = 90 8 Finl speed, v = 0 ms Accelertion = 0. ms Distnce covered, S =? = ms Using the reltion v u = S, we hve v -u 0-() S+ = = 6 m (-0.) Ex.8 A trolley, while going down n inclined plne, hs n ccelertion of cms. Wht will be its velocity Sol. s fter the strt? Given Initil velocity, u = 0 Finl velocity, v =? Time, t = s Accelertion, = cms We know tht v = u + t Or v = 0 + = 6 cms Therefore, finl velocity = 6 cms. : , url : : info@motioniitjee.com

28 Pge # 8 MOTION Ex.9 A rcing cr hs uniform ccelertion of 4 ms. Wht distnce will it cover in 0 s fter strt. Sol. Given Initil velocity, u = 0 Accelertion, = 4 ms Time, t = 0 s Distnce covered, S =? We know ; S = ut + t S = (0) = = 00 m Therefore, distnce covered = 00 m. Ex.0 A stone is thrown in verticlly upwrd direction with velocity of ms. If the ccelertion of the stone during its motion is 0 ms in the downwrd direction, wht will be the height ttined by the stone nd how much time will it tke to rech there? Sol. Given Initil velocity, u = ms Finl velocity, v= 0 Accelertion in the downwrd direction = 0 ms Therefore ccelertion in the upwrd direction = 0 ms Height ttined by stone, S =? Time tken to ttin height, t =? (i) (ii) Using the reltion ; v = u + t 0 = + ( 0) t or t = /0 = 0. s Using the reltion ; v u = S, we hve v -u (0) - () S = = =. m (-0) Ex. An rtificil stellite is moving in circulr oribit of rdius 40 km. Clculte its speed if it tkes 4 hours to revolve round the erth. Sol. R = 40 km. t = 4 hrs. v =? V = r t = 40 4 v =.07 km/sec. Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

29 MOTION Pge # 9 Q. An thlete completes one round. of circulr trck of dimeter 00 m in 40 s. Wht will be the distnce covered nd the displcement t the end of minutes 0 s? Ans. Given Dimeter of circulr trck, r =00 m Circumference of circulr trck = s = (r) = NCERT QUESTIONS WITH SOLUTIONS m 7 7 Time for completing one round = 40 s. Time for which the thlete rn = min nd 0 s = 40s r s = 4400 m 7 Distnce covered in s = 4400 m 7 40 (i) Therefore, distnce covered by thlete in 40s = m 7 40 (ii) As the thlete returns to the initil point in 40s, his displcement = 0 Now, Number of rounds in 40 seconds = Hence number of rounds in 40s is = For ech complete round the displcement is zero. Therefore for complete rounds, the displcement will be zero. A r B The finl displcement will be due to hlf the round (i.e. semicircle). Thus, his displcement = dimeter of circulr trck = 00 m. Q. Joseph jogs from one end A to the other end B of stright 00 m rod in minutes 0 seconds nd then turns round nd jogs 00 m bck to point C in nother minute. Wht re Joseph s verge speeds nd velocities in jogging () from A to B nd (b) from A to C? Ans. The required figure is s shown A C B 00m 00m () Distnce covered = 00m Time tken = min nd 0s = 70 s Now verge speed from A to B is given by V v = dis tn ce cov ered 00.76ms time 70 Now verge velocity from A to B is given by V v = displcement 00.76ms time 70 : , url : : info@motioniitjee.com

30 Pge # 0 MOTION (b) When Joseph turns round from B to C towrds west, then Distnce covered = = 400 m Time tken = = 0s Therefore, verge speed from A to C is V v = dis tnce cov ered ms time 0 Now displcement from A to C = 00m Therefore, verge velocity from A to C is V v = displcement 00 time ms Q. Abdul while driving to school computes the verge speed for his trip to be 0 km h. On his return trip long the sme route, there is less trffic nd the verge speed is 40 km h. Wht is the verge speed for Abdul's trip? Ans. Let one wy distnce for his trip be s. Let t be the time for his trip from home to school nd t be the time for his return trip. Then t = S S h, v 0 nd t = S S h v 40 Therefore, totl time of trip is T = t + t = S S S h Totl distnce covered = S Therefore, verge speed of Abdul V v = totldis tn ce totl time = S 40 S = 6.6 kmh Q.4 A motorbot strting from rest on lke ccelertes in stright line t constnt rte or.0 ms for 8.0 s. Hew fr does the bot trvel during this time? Ans. Given, initil velocity of bot, u = 0 Accelertion, =.0 m s Time, t = 8s Distnce covered, s =? Using the reltion s = ut + t we hve, s = = 96m. Q. The driver of cr trvelling t km h pplies the brkes nd ccelertes uniformly in the opposite direction. The cr stops in s. Another driver going t kmh in nother cr pplies his brkes slowly nd stops in 0s. On the sme grph pper, plot the speed versus time grphs for the two crs. Which of the two crs trvelled fther fter the brkes were pplied? Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

31 MOTION Pge # Ans. The speed time grph of both the crs re shown below. (i) Distnce covered by cr moving t kmh (or 8 = 4.4 ms ) = re of PQR = PO OQ = 4.4 = 6 m P L Q N O 0 time (sec.) (ii) Distnce covered by cr moving t kmh (or 8 = 0.8 ms ) = re of PLN = LO ON = = 4. m The cr moving t km h trvels more distnce on the ppliction of brkes. Q.6 Figure below shows the distnce-time grph of three objects A, Bnd C. Study the grph nd nswer the following questions: () Which of the three is trvelling the. fstest? (b) Are ll three ever t the sme point on the rod? (c) How fr hs C trvelled when B psses A? (d) How fr hs B trvelled by the time it psses C? B C A 8 P Q time (hour) Ans. () Cr B is trvelling the fstest, becuse its slope is lrgest mong the three. (b) No, they re never t the sme point becuse U the grphs of A, Bnd C do not intersect t one point. (c) When cr B psses cr A t point P, the distnce covered by cr C = 8 = 6 km. (pprox.) (d) Cr B nd C pss ech other t point Q. The distnce trvelled by B t tht point is nerly.7 km. : , url : : info@motioniitjee.com

32 Pge # MOTION Q.7 A bll is gently dropped from height of 0 m. If its velocity Increses uniformly t the rte of 0 ms, with wht velocity will it strike the ground? After wht time will it strike the ground?. Ans. Given, initil velocity of bll, u = 0 Finl velocity of bll, v =? Distnce through which the bll flls, s = 0 m Accelertion = 0 ms Time of fll, t =? We know v u = s or v 0 = 0 0 = 400 or v = 0 ms Now using v = u + t we hve 0 = t or t = s Q.8 The speed-time grph for cr is shown in figure below. () Shde the re on the grph tht represents the distnce trvelled by the cr during the first 4 seconds. (b) Which prt of the grph represents uniform motion of the cr? Ans. () During first 4 seconds, cr is moving with nonuniform ccelertion. Are of shded portion represents distnce trvelled. (b) The stright line portion of the grph represents uniform motion of the cr. Q.9 Stte which of the following situtions re possible nd give n exmple for ech of these; Ans. () An object with constnt ccelertion but with zero velocity. (b) An object moving in certin direction with ccelertion in the perpendiculr direction. () A body with constnt ccelertion but with zero velocity is possible. For exmple, when body is just relesed, its initil velocity u = 0, but ccelertion g = 0 ms. (b) It is possible. When stone, tied to string, is whirled in circulr pth, the ccelertion cting on it is lwys t right ngle to the direction of motion of stone. Q.0 An rtificil stellite is moving in circulr orbit of rdius 40 km. Clculte its speed if it tkes 4 hours to revolve round the erth. Ans. Distnce covered by the stellite in 4 hours S = r = km 7 Therefore speed of stellite v = dis tn ce trvelled 67.4 time tken kms Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

33 MOTION Pge # EXERCISE I BOARD PROBLEMS Q. Distinguish between speed nd velocity. Q. Wht does the pth of n object look like when it is in uniform motion? Q. Under wht condition will the displcement nd distnce hve the sme mgnitude? Q.4 A boy hits footbll high up into the ir. He runs nd ctches the foot bll before it hits the ground. Which of the two, the boy or the footbll hs hd greter displcement? Q. Cn the speed of body be negtive? Q.6 Wht is the verge velocity of prticle when it returns to the strting point? Cn its verge speed by zero? Q.7 A cr mnufcturer dvertises tht the brkes re so perfect tht the cr stops instntneous. Comment. Q.8 Give n exmple of body which covers certin distnce, but its displcement is zero? Q.9 Cn the displcement of prticle be zero when the distnce trvelled is not zero? Q.0 Wht is the reltion between distnce nd time (i) when body is moving with uniform speed? (ii) when body is moving with vrible speed? Q. Drw velocity-time grphs for the following situtions : (i) When body is moving with uniform velocity. (ii) When body is moving with vrible velocity, but uniform ccelertion (iii) When body is moving with vrible velocity, but uniform retrdtion (iv) When body is moving with vrible velocity nd vrible ccelertion Q. Distinguish between terms distnce nd displcement. Q. Mention some uses of velocity time grphs. Q.4 A trin strting from rilwy sttion nd moving with uniform ccelertion ttins speed 40 km h in 0 minutes. Find its ccelertion. Q. A bus strting from rest moves with uniform ccelertion of 0. ms for minutes. Find () the speed cquired, (b) the distnce trvelled. Q.6 A driver of cr trvelling t kmh pplies the brkes nd ccelertes uniformly in the opposite direction. The cr stops in s. Another driving going t kmh in nother cr pplies his brkes slowly nd stops in 0s. On the sme grph pper, plot the speed versus time grphs for the two crs. Which the two crs trvelled frther fter the brkes were pplied. Q.7 A trin is trvelling t speed of 90 kmh. Brkes re pplied so s to produce uniform ccelertion of 0. ms. Find how fr the trin will go before it is brought to rest. Q.8 An thlete completes one round of circulr trck of dimeter 00m in 40s. Wht will be the distnce covered nd the displcement t the end of minutes 0 s? Q.9 An eroplne lnds t 6 kmh nd stops fter covering runwy of km. Clculte the ccelertion nd the time, in which it comes to rest. Q.0 A truck running t 90 kmh is brought to rest over distnce of m. Clculte the retrdtion nd time for which brkes re pplied. : , url : : info@motioniitjee.com

34 Pge # 4 Q. A motor bike running to 90 kmh, is slowed down to 4 kmh by the ppliction of brkes, over distnce of 40m. If the brkes re pplied with the sme force, clculte (i) totl time in which bike comes to rest (ii) totl distnce trvelled by bike. Q. A person trvels distnce of m towrds est, then 4 m towrds north nd then m towrds west. MOTION Q.6 Figure below shows the distnce-time grph of three objects A, Bnd C. Study the grph nd nswer the following questions: () Which of the three is trvelling the. fstest? (b) Are ll three ever t the sme point on the rod? (c) How fr hs C trvelled when B psses A? (i) (ii) Clculte the totl distnce trvelled. Clculte the resultnt displcement. (d) How fr hs B trvelled by the time it psses C? Q. A body is moving in stright line. Its distnces from origin re shown with time in Fig. A, B, C, D nd E represent different prts of its motion. Find the following : 8 P B C A (i)displcement of the body in first seconds. (ii) Totl distnce trvelled in 7 seconds. 4 Q (iii) Displcement in 7 seconds time (hour) B C D 40 A 0 E O Time (s) Distnce-time grph Q.7 A bus strting from rest moves with unifor m cce le rtion of 0. ms for minutes. Find () the speed cquired. Q.4 The distnce between two points A nd B is 00 m. A person moves from A to B with speed of 0 m/s nd from B to A with speed of m/s. Clculte verge speed nd verge velocity. Q. A cr moves with speed of 40 km/hr for first hour, then with speed of 60 km/hr for next hlf hour nd finlly with speed of 0 km/hr for next hours. Clculte the (b) the distnce trvelled. Q.8 A trin strting from rilwy sttion nd moving with uniform ccelertion ttins speed 40 kmh in 0 minutes. Find its ccelertion. Q.9 From the top of tower of height 490 m, shell is fired horizontlly with velocity 00 m/s. At wht distnce from the bottom of the tower, the shell will hit the ground? verge speed of the cr. Corporte Hed Office : Motion Eduction Pvt. Ltd., 94 - Rjeev Gndhi Ngr, Kot- (Rj.)

35 MOTION Q.0 The brkes pplied to cr produce negtive ccelertion of 6 m/s. If the cr tkes seconds to stop fter pplying the brkes, clculte the distnce it trvels during this time. Q. Strting from rest, Deepk pddles his bicycle to ttin velocity of 6 m/s in 0 seconds then he pplies brkes so tht the velocity of the bicycle comes down to 4 m/s in the next seconds. Clculte the cce lertion of the bicycle in both the cses. Q. A body strts moving with n initil velocity 0 m/s nd ccelertion 0 m/s. How much distnce it will cover in 4s? Also, clculte its verge speed during this time intervl. Q. A body is moving with speed of 0 m/s. When certin force is pplied, n ccelertion of 4 m/s is produced. After how much time its velocity will be 80 m/s? Pge # Q.4 A body strts from rest nd moves with constnt ccelertion. It trvels distnce s in first 0 s, nd distnce s in next 0 s. Find the reltion between s nd s. Q. A trin is moving with velocity 400 m/s. With the ppliction of brkes retrdtion of 0 m/s is produced. Clculte the following : (i) After how much time it will stop? (ii) How much distnce will it trvel before it stops? Q.6 A body is thrown verticlly upwrds with n initil velocity of 9.6 m/s. If g = 9.8 m/s. Clculte the following : (i) The mximum height ttined by the body. (ii) After how much time will it come bck to the ground? : , url : : info@motioniitjee.com