KINEMATICS The branch of physics which deals with the study of motion of material objects without discussing its causes (forces) is called kinematics.

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1 CHP # KINEMATIC KINEMATIC The branch o physcs whch deals wh he sudy o moon o maeral objecs whou dscussng s causes (orces) s called knemacs. Q.1 Dene moon and res wh example? A. Moon When a body changes s poson wh respec o s surroundng, we say ha he body s n moon. For example a body "B" changes s poson wh respec o anoher body "A", we say ha body "B" s n moon. Res When a body does no change s poson wh respec o s surroundng, we say ha he body s a res. For example a body "B" does no change s poson wh respec o anoher body "A", we say ha body "B" s a res. Q. Wre ypes o moon wh examples? A. There are hree ypes o moon whch are saed as; (1) Translaory moon A ype o moon n whch each and every parcle o he body move n he same manner as ha o every oher parcle. For examples () Moon o he cars () Moon o he lyng brds () Moon o he allng objecs () Roaory moon A ype o moon n whch a body roae abou a xed pon and he dsance o he body a any me s consan (equal) o he xed pon. For examples () Moon o he wheel o a cycle () Moon o he hands o a clock () Moon o he wngs o a an. (3) braory moon The To and ro moon o an objec around a x pon known as mean or equlbrum poson s called braory moon. For examples () Moon o a swng. () Moon o a smple pendulum. () Moon o mass aached o a sprng. Q.3 Derenae beween dsance and dsplacemen? A. Dsance The lengh cover by a body on deren pahs s called dsance. I s a scalar physcal quany. I s denoed by "". Is I un s meer (m).

2 Dsplacemen The shores dsance beween wo pons s called dsplacemen. I s a vecor physcal quany. I s denoed by "". Is I un s meer (m). Q.4 Dene speed and s dervaves? A. peed The dsance covered by a body n un me s called speed. I s denoed by "". I s a scalar physcal quany. Mahemacally Ds an ce peed me Is I un s meer/second (m/s). Dervaves o he speed are; () () () Average speed I can be dened as "he oal dsance covered dvded by oal me aken s called average speed". Mahemacally <> = Insananeous speed I can be dened as "he me rae o change dsance covered by a body s called Insananeous speed". Mahemacally ns Unorm speed I can be dened as " a body covers equal dsance n equal nerval o me, hen he speed o he body s called unorm speed". Q.5 Dene elocy and s dervaves? A. elocy The dsplacemen covered by a body n un me s called elocy. I s denoed by "". I s a vecor physcal quany. Mahemacally Dsplacemen elocy me Is I un s meer/second (m/s). () Dervaves o he elocy are; Average elocy I can be dened as "he oal dsplacemen covered dvded by oal me aken s called average elocy". Mahemacally

3 () () < > = Unorm elocy I can be dened as " a body covers equal dsplacemen n equal nerval o me, hen he elocy o he body s called unorm elocy". OR I he speed as well as drecon o he body does no change n a me nerval, hen he elocy o he body s called unorm elocy. arable elocy I can be dened as "I he speed or drecon or boh o he body changed n a me nerval, hen he elocy o he body s called varable elocy. Q.6 Dene Acceleraon and s dervaves? A. Acceleraon I can be dened as "he me rae o change o elocy s called acceleraon". I s dened by "a". I s a vecor physcal quany. Mahemacally a = () () () Is I un s meer per second per second (m/s ). Dervaves o he acceleraon are; Posve acceleraon I can be dened as " he magnude o elocy ncreases wh me, hen acceleraon s called posve acceleraon". Negave acceleraon I can be dened as " he magnude o elocy decreases wh me, hen acceleraon s called negave acceleraon". Average acceleraon I can be dened as "he change n elocy dvded by me nerval s called average acceleraon". Mahemacally a Q.7 Dene scalars and vecors wh examples? A. calars Those physcal quanes whch are compleely speced rom s magnude (number+proper un) are called scalars. For examples Lengh, mass, me, speed, area, volume, ec.

4 ecors Those physcal quanes whch are compleely speced rom s magnude (number+proper un) as well as drecon are called vecors. For examples Dsplacemen, elocy, acceleraon, Force, Momenum, orque, ec. Q.8 How a vecor can be represened? A. A vecor can be represened by he ollowng wo mehods. () () ymbolc represenaon In hs mehod a vecor can be represened by a leer. An arrow head s placed above or below he leer. OR he leer s wren as bold ace For example a vecor A can be saed as; A, A, A Graphcal represenaon Graphcally a vecor can be represened by a sragh lne havng an arrow head n he drecon o he vecor. Ths process s compleed n he ollowng our seps: 1. elec a suable scale.. Draw NEW or coordnae sysem. 3. Draw a 5cm represenave lne on he NEW. 4. Draw he requred lne accordng o he drecon. Example Al Khald ank s movng wh a velocy o 100Km/h owards norh eas. Draw represenave lne o s velocy? oluon N 1. cale 0Km/h = 1cm 100Km/h = 5cm W E. Draw NEW sysem 3. Represenave lne on he NEW. N 5cm W O 45 o E

5 4. Requred lne O 5cm 45 o E Q.9 Wha s graph? How a graph can be drawn. A. Graph I s a mehod o show he relaonshp beween wo physcal quanes. For example Dsance-me graph shows ha how speed or elocy o a body changes. A graph s drawn on a graph paper. Graph paper conans horzonal and vercal lnes o equal dsances. We use Recangular coordnae sysem or graph, whch conss o wo muually perpendcular lnes XOX and YOY. As shown below n gure; Q.10 How we can deermne he slope o a graph? A. The slope o a graph can be deermned as ollow; () Take wo pons P 1( x1, y1) and P ( x, y) on he graph. () Draw perpendculars on he x-axs and y-axs rom boh pons. () Calculae he derence n x and y coordnaes as; x x x 1 and y y y1 (v) Dvde y by x ; hs s he slope o he graph. Mahemacally y y lope = = y1 x x x1

6 Q.11 Wha s Dsance-me graph? A. Dsance- me graph A graph whch shows he relaonshp beween dsance and me s called Dsance-me graph. The dsance raveled s aken on he vercal axs (y-axs) whle he me s aken on he horzonal axs (x-axs). The slope o he graph denoes speed or elocy. Mahemacally lope = y y = y1 x x x1 Dsance (m) lope peed or elocy = y y = y1 x x x1 Q.1 Wha s peed-me graph? A. peed- me graph A graph whch shows he relaonshp beween speed and me s called speedme graph. The speed s aken on he vercal axs (y-axs) whle he me s aken on he horzonal axs (x-axs). The slope o he graph denoes acceleraon. Mahemacally O Tme (sec) lope = y y = y1 x x x1 peed (m/s) lope Acceleraon = y y = y1 x x x1 O Tme (sec) Q.13 How he dsance raveled can be deermned rom speed-me graph? A. The dsance raveled can be calculaed rom he speed-me graph by he area enclosed he graph. For example Consder a body moves wh unorm speed, s nal speed s OA. Aer a me nerval OC he speed o he body becomes BC. The graph can be drawn as; Mahemacal orm As we know ha B C s clear rom gure, ha = OA, = OC = OA x OC peed (m/s) = Wdh x Lengh O Tme (s) A

7 = Area o recangle OABC = Area o he graph Q.14 Prove rs equaon o moon ( a ) by graph? A. aemen Consder he speed-me graph n whch he nal speed o he body s "OA". Aer a me nerval "OC" he speed o he body changes unormly and becomes "BC". The slope o he graph "AB" shows acceleraon "a". Fgure Y a B A D O Mahemacal proo I s clear rom gure ha BC OA BD BD (1) To nd BD, we have BD lope o graph AB = AD BD a a BD Pu he value o BD n equaon (1) a C X

8 1 Q.15 Prove second equaon o moon ( a ) by graph? A. aemen Consder he speed-me graph n whch he nal speed o he body s "OA". Aer a me nerval "OC" he speed o he body changes unormly and becomes "BC". The slope o he graph "AB" shows acceleraon "a". The dsance raveled by he speed me graph can be calculaed as; Dsance raveled = Area enclosed by he graph Fgure Y B a a A D X O C Mahemacal proo I s clear rom gure ha = Area o OABC Bu = Area o recangle OADC + Area o rangle ABD = OAOC + 1 (AD BD) 1 ( )( a) 1 a Q.16 Prove hrd equaon o moon (a ) by graph? A. aemen Consder he speed-me graph n whch he nal speed o he body s "OA". Aer a me nerval "OC" he speed o he body changes unormly and becomes "BC". The slope o he graph "AB" shows acceleraon "a".

9 Fgure Y B a A D O Mahemacal proo C I s clear rom gure ha = Area o OABC = Area o Trapezum OABC We know ha Area o Trapezum = (sum o parallel sdes o Trapezum) AD ( OA BC) OC ( ) ( ) ( A) Bu rom rs equaon o moon; a a Pu he value o n equaon (A); We ge = ( ) ( ) a a X hegh

10 Q.17 Wha s mean by gravaonal acceleraon? A. Gravaonal acceleraon An Ialan scens Galleo drop several objecs ro he amous Leanng ower a he same me. He concluded ha all he objecs reached a he same me owards he earh surace. He saed ha earh arac every objec sel wh he same acceleraon called gravaonal acceleraon. I s denoed by g. Is value s 9 8m / s a he surace o he earh. Equaons o moon or moon under gravy are; g 1 g gh CONCEPTUALQUETION (1) The gure gven shows he speed me graph or a pendulum. Wre down (a) The maxmum speed. (b) The me a whch he maxmum speed occurs. (Ans) (a) The maxmum speed s 1m/s. (b) The me a whch maxmum speed occur s 0 3ec. () Can a body a res be regarded n a sae o moon? Gve example (Ans) Yes a body a res can be regarded n a sae o moon. For example A person sng n a ran s a res wh respec o an observer n he ran bu hs person s n moon or he observer ousde he ran. (3) Is he dsance covered by he body may be greaer han he magnude o dsplacemen? (Ans) Yes he dsance covered by a body may be greaer han he dsplacemen. For example When an objec s movng on a crcular pah s dsance covered s greaer han he dsplacemen a any nsan o me. (4) Is possble ha dsplacemen s zero bu no he dsance? (Ans) Yes s possble ha dsplacemen s zero bu no he dsance. When an objec moves n a crcle and complee one round rp s dsplacemen become zero whle he dsance covered s no zero.

11 (5) Under wha condon dsplacemen s equal o he dsance? (Ans) The dsplacemen and dsance covered s equal and only he body s movng n a sragh lne. (6) Can a body have acceleraon wh zero velocy? (Ans) A body has no acceleraon wh zero velocy. Because acceleraon s produce when he velocy o he body s changed. Mahemacally a 0 a a 0m / s (7) Can he speed o a body be negave? (Ans) No he speed o he body can no be zero. Because s a scalar quany and scalar quanes can no be negave. (8) Is possble ha velocy o an objec be n a drecon oher han he drecon o acceleraon? (Ans) Yes he velocy o a body can be n a drecon oher han acceleraon. For example When a body moves n a crcle, he drecon o lnear velocy s angen o he crcle whle he acceleraon s dreced owards he cenre o he crcle. a (9) Is he knemacs equaon consan? (Ans) No he knemacs equaon consan. 1 a rue acceleraon s no 1 a s no rue acceleraon s no

12 (10) By gvng an example prove ha res and moon are relave erms. (Ans) Moon and res are relave. For example wo persons are seng n a bus. They are a res wh respec o each oher. Bu due o he moon o he bus, hey are n moon wh respec o her exernal surroundng. (11) Gve an example o an acceleraed body movng wh a unorm speed. (Ans) The moon o a body n a crcle wh unorm speed have an acceleraon due o change n he drecon o velocy called cenrpeal acceleraon. a (1) Is un Kmh -1 s -1 s same as Kms -1 h -1 explan? (Ans) The un Kmh -1 s -1 s no he same as Kms -1 h -1. Because n un Kmh -1 s -1, Kmh -1 s he un o velocy he change o whch s gven n second. Bu n he un Kms -1 h -1, Kms -1 s he un o velocy he change o whch s n hour. (13) I bus s ravelng easward, can s acceleraon be wesward? Explan (Ans) Yes a bus ravelng easward s acceleraon can be wesward. Explanaon A bus s ravelng easward, he velocy o he bus decreasng connuously, hen he deceleraon s produce whch wll be wesward. (14) I an objec s saonary s s acceleraon necessary zero? (Ans) Yes an objec s saonary s acceleraon s zero. Because he speed o he body s zero and drecon s unchanged. (15) When he velocy me graph s a sragh lne parallel o me axs, wha can you say abou s acceleraon. (Ans) The acceleraon o he body s zero. Because he graph shows ha velocy s consan. When he velocy o he body s consan s acceleraon wll be zero. (16) A ball s hrown vercally upward wh an nal speed o 5m/s. Wha wll s speed be when reurns o s sarng pon. (n he absence o ar ressance).

13 (Ans) The body reurns o s sarng pon wh he same speed o 5m/s n he absence o ar ressance. NUMERICAL PROBLEM (1) A bus ravel 15Km owards wes makes u-urn back ravel a urher dsance o 10Km, nd (a) Dsance raveled b) Is dsplacemen Gven daa 1 = 15Km = 10Km a) Dsance, =? = 1 + = =5Km b) Dsplacemen, =? = - 1 = = 5Km ---- owards eas o sarng pon. () A race car ravels around a crcular rack, coverng a dsance o 850m n 5s beore soppng a pon rom where sared. Deermne he average elocy o he car durng hs perod o me. Gven daa Dsance, = 850m Dsplacemen, = 0m Tme, = 5s Average velocy, =? We know ha 0 5 0m =850m 0m 5sec

14 (3) A ruck movng a a speed o 0m/s begns o slow a consan rae o 3m/s, nd how ar goes beore soppng? Gven daa 0m? 0m a 3m We know ha a 0 a (0) ( 3) m (4) The speed o a bus s reducng unormly rom 15m/s o 7m/s. whle ravelng a dsance o 90m. (a) Fnd he acceleraon (b) How much urher dsance wll he bus ravel beore comng o res, provded he acceleraon remans consan? Gven daa 15m 7m 90m a (a)? We know ha a a (7) (15) a a a 0 977m

15 (b) 7m 0m a 0 977m? We know ha a a (0) (7) ( 0 977) m (5) Brakes are appled o a ran ravelng a 7Km/h aer passng over 00m s velocy s reduced o 36Km/h a he same rae o reardaon, how much urher wll go beore s brough o res? Gven daa 71000m 7Km / h 0m 3600sec m 36Km / h 10m 3600sec 00m Re ardaon a?? When 10m 0m To nd he reardaon rs

16 a a (10) (0) a a m / s 400 Now o nd he urher dsance raveled a a 0 (10) ( 0 75) m (6) A moor cycls s movng on a road wh an acceleraon o 3m/s, how much me wll requre o change he velocy rom 10m/s o 0m/s? Gven daa a 3m? 10m 0m We know ha

17 10 3 a a a sec (7) A cycls sars rom res and moves wh unorm acceleraon o 0.m/s aer mnues, nd he velocy o he cycls and dsance covered. Gven daa 0m a 0 m?? mn 60sec 10sec We know ha a 0 (0 )(10) m We also know ha 1 a (0 )(10) 1 (0 )(14400) 1440m

18 (8) A body s hrown vercally upward wh a speed o 0m/s. How hgh wll rse? (ake downward g=10m/s ) Gven daa 0m g 10m h? 0m We know ha gh h h h h g m 0 (0) ( 10)