PSW-4-Motion Worksheet Name:. Class #:

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1 Speed, Velocity, nd Accelertion PSW-4-1 Vocbulry Distnce: Displcement: Speed: Velocity: Accelertion: How fr something trvels. How fr something trvels in given direction. How fst something is moving. How fst something is moving in given direction. The rte t which the velocity chnges during given mount of time. Distnce vs. Displcement Notice tht Distnce nd Displcement re very similr. Distnce is n exmple of wht we cll sclr quntity. In other words, it hs mgnitude, but no direction. Displcement is n exmple of vector quntity becuse it hs both mgnitude nd direction. The SI unit for distnce nd displcement is the meter (m). Displcements smller thn meter my be expressed in units of centimeters (cm) or millimeters (mm). Displcements much lrger thn meter my be expressed in units of kilometers (km).

2 Speed vs. Velocity Averge Speed = distnce time Distnce = Averge Speed Time Time = distnce Averge Speed Also cn be expressed s Averge Speed = d f d 0 t f t 0 d f d 0 = Averge Speed t f t 0 t f t 0 = d f d 0 Averge Speed where df nd tf re the finl position nd time respectively, nd do nd to re the initil position nd time. The symbol Δ (delt) mens chnge so Δd is the chnge in position, or the displcement, while Δt is the chnge in time. The SI unit for both speed nd velocity is the meter per second (m/s). When trveling in ny moving vehicle, you rrely mintin the sme velocity throughout n entire trip. If you did, you would trvel t constnt speed in stright line. Insted, speed nd direction usully vry during your time of trvel. If you begin nd end t the sme loction but you trvel for gret distnce in getting there (for exmple, when you trvel in circle), you hve mesurble verge speed. However, since your totl displcement for such trip is zero, your verge velocity is lso zero. In this chpter, both verge speed nd verge velocity will be written s vv. The v subscript will be dropped in lter chpters. Accelertion = v t v = t t = v Also cn be expressed s = v f v 0 v t f t f v 0 = (t f t 0 ) t f t 0 = v f v 0 0 where the terms vf nd vo men finl velocity nd initil velocity, respectively. The SI unit for ccelertion is the meter per second squred (m/s 2 ). If the finl velocity of moving object is smller thn its initil velocity, the object must be slowing down. A slowing object is sometimes sid to hve negtive ccelertion becuse the mgnitude of the ccelertion is preceded by negtive sign.

3 1. On My 29, 2005, Dnic Ptrick ws nmed the first femle Indy 500 Rookie of the Yer fter her 4th plce finish; the best Indy 500 finish of ny womn in the event s history. Dnic completed the rce in time of h. Wht ws Dnic s verge speed during the mi rce? NOTE: Generlly the unit miles is not used in physics exercises. However, the Indinpolis 500 is rce tht is mesured in miles, so the mile is pproprite here. Don t forget, the SI unit for distnce is the meter. Known Need to Know Δd=500.0 mi Vv=? v v = d t = mi h = mi h or mi/h Δt=3.174 h v v = d t 2. The slowest niml ever discovered ws crb found in the Red Se. It trveled with n verge speed of 5.70 km/yer. How long would it tke this crb to trvel 100. km? t = t = d v v 100 km km yr = km/yr km Known Δd=100.0 km Vv=5.70 km/yer t = d v v Need to Know Δt=? 17.5 yrs Answer: Time it tkes for the crb s trip (3pts) 3. The peregrine flcon is the world s fstest known bird nd hs been clocked diving downwrd towrd its prey t constnt verticl velocity of 97.2 m/s. If the flcon dives stright down from height of 100. m, how much time does this give rbbit below to consider his next move s the flcon begins his descent? t = d v v t = 100 m m sec = m/s m 1.03 sec Answer: Time it tkes the flcon to dive

4 4. Benjmin wtches thunderstorm from his prtment window. He sees the flsh of lightning bolt nd begins counting the seconds until he hers the clp of thunder 10. s lter. Assume tht the speed of sound in ir is 340 m/s. How fr wy ws the lightning bolt. ) in m? 340 m 10. s d = v v t = ( ) ( ) = 3, 400m s 1 b. in km? NOTE: The speed of light, 3.0 X 10 8 m/s, is considerbly fster thn the speed of sound. Tht is why you see the lightning flsh so much erlier thn you her the clp of thunder. In ctulity, the lightning nd thunder clp occur lmost simultneously m km 1000 m = 3. 4 km The lightning bolt is 3.4 km wy, which is just little over two miles for those of you who think in English units! 5. Hns stnds t the rim of the Grnd Cnyon nd yodels down to the bottom. He hers his yodel echo bck from the cnyon floor 5.20 s lter (hint: the sound trvels down AND bck, in 5.20 s!!!). Assume tht the speed of sound in ir is m/s. How deep is the cnyon t this loction? d = v t Known Vv=340 m/s Δt=10.0 s d = v t Need to Know Δd=? d = 340 m s 5.2 s 2 = 884 m s s 884 m Answer: Depth of the cnyon

5 6. The world speed record on wter ws set on October 8, 1978 by Ken Wrby of Blowering Dm, Austrli. If Ken drove his motorbot distnce of m in s, how fst ws his bot moving c. in m/s nd d. in mi/h? (Hint: 1 mi=1609 m) [look t exmple on #4] v v = d t v v = 1000m 7.045s = m/s m 1 mi 60 s 60 min s 1609 m 1 min 1 hr = mi/hr m/s mi/h Answer: speed m/s speed mi/h (3 pts) (2pts) 7. According to the World Flying Disk Federtion, the world distnce record for flying disk throw in the men s 85-yers-nd-older ctegory is held by Jck Roddick of Pennsylvni, who on July 13, 2007, t the ge of 86, threw flying disk for distnce of 54.0 m. If the flying disk ws thrown horizontlly with speed of 13.0 m/s, how long did the flying disk remin loft? (Jck Roddick ws lso physics techer! t = d v v t = 54m m s = m/s s 4.15 sec Answer: Time the flying disk remined loft 8. Grce is driving her sports cr t 30 m/s when bll rolls out into the street in front of her. Grce slms on the brkes nd comes to stop in 3.0 s. Wht ws the ccelertion of Grce s cr? = 0 m s 30.m s = 30. m s = 30.m t f t s 0 s 3.0 s 3.0 s = v f v 0 2 = 10 m/s2 The negtive sign mens the cr ws slowing down. Known Need to Know v0=30 m/s =? vf=0 m/s tf=3.0 s t0=0 = v f v 0 t f t 0

6 9. A jumbo jet txiing down the runwy receives word tht it must return to the gte to pick up n importnt pssenger who ws lte to his connecting flight. The jet is trveling t 45.0 m/s when the pilot receives the messge. Wht is the ccelertion of the plne if it tkes the pilot 5.00 s to bring the plne to hlt? Known Need to Know = = v f v 0 t f t 0 (0 45) m/s (5 0)s = 9 m s s v0=45.0 m/s vf=0 m/s tf=5.0 s t0=0 s = v f v 0 t f t m/s 2 Answer: Accelertion of the plne (3 pts) Slowing down Answer: Is the plne speeding up or slowing down? (1 pt) It hs negtive ccelertion Answer: How do you know? (2 pts) 10. While driving his sports cr t 20.0 m/s down four-lne highwy, Eddie comes up behind slow-moving dump truck nd decides to pss it in the left-hnd lne. If Eddie cn ccelerte t 5.00 m/s 2, how long will it tke for him to rech speed of 30.0 m/s? =? t = v f v 0 t = (30 20) m/s (10) m s2 5 m/s 2 = = 2 s 5 m s 2.00 sec Answer: Time it tkes to rech pssing speed 11. A cterpillr crwling up lef slows from 0.75 cm/s to 0.50 cm/s t rte of cm/s 2. How long does it tke the cterpillr to mke the chnge? t = v f v 0 ( ) cm/s ( 0.25) m s2 t = 0.05 cm/s 2 = = 5 s 0.05 m s 5 sec Answer: Time it tkes to mke the chnge in speed

7 12. Vivin is wlking to the hirdresser s t 1.3 m/s when she glnces t her wtch nd relizes tht she is going to be lte for her ppointment. Vivin grdully quickens her pce t rte of m/s 2. Wht is Vivin s speed fter 10.0 s? v f v 0 = t v f 1.3 m s = 0.09 m s 2 10s v f 1.3 m s m s = (0.09 m s 2 10s) m s v f = (0.09 m s 2 10s) m = 2.2 m/s s 2.2 m/s Answer: Vivin s finl speed 13. A torpedo fired from submerged submrine is propelled through the wter with speed of m/s nd explodes upon impct with trget m wy. e. If the sound of the impct is herd s fter the torpedo ws fired, wht is the speed of sound in wter? (Becuse the torpedo is held t constnt speed by its propeller, the effect of wter resistnce cn be neglected.) t torpedo = t torpedo = 2000 m 20 m/s d v torpedo = 100 s t totl t torpedo = t sound s 100 s = t sound = 1.4 s v sound = v sound = 2000 m/s 1.4 s d t sound = m/s Known Torpedo s distnce d= m Torpedo s speed v=20.00 m/s Time of torpedo nd the time of the sound to return seconds Need to Know Δttorpedo=? Δtsound=? Speed of sound only Vsound= 1430 m/s Answer: Speed of sound (3 pts)

8 Free Fll PSW-4-2 Vocbulry Free Fll: The movement of n object in response to grvittionl ttrction. When n object is relesed, it flls towrd Erth due to the grvittionl ttrction Erth provides. As the object flls, it will ccelerte t constnt rte of 9.8 m/s 2 regrdless of its mss. However, to mke clcultions more expedient nd esier to do without clcultor, this number will be written s g = 10.0 m/s 2 throughout this course. There re mny different wys to solve free fll exercises. The sign convention used my be chosen by you or your techer. In this book, the downwrd direction will be positive, nd nything flling downwrd will be written with positive velocity nd position; nything moving upwrd will be represented with negtive velocity nd position. Remember: Grvity lwys cts to pull n object down, so the grvittionl ccelertion, g, will lwys be written s positive number regrdless of which direction the object is moving. The displcement nd finl velocity of flling object is written s Moving Object [verticl]: d = v 0 t t2 [displcement] v f = v 0 + t [velocity] Since grvity g is n ccelertion, g cn be substituted for, you will then hve d = v 0 t + 5t 2 [displcement] v f = v t [velocity] Note tht the term g in ll of these exercises cn be written s if you use constnt ccelertion other thn grvity. Therefore, these equtions cn be used for objects moving horizontlly s well s verticlly. It is common to neglect ir resistnce in most free fll exercises (including those in this course), lthough in rel life, ir resistnce is fctor tht must be tken into ccount. This course will lso ssume tht the initil speed of ll objects in free fll is zero, unless otherwise specified.

9 1. King Kong crries Fy Wry up the 321-m-tll Empire Stte Building. At the top of the skyscrper, Fy Wry s shoe flls from her foot. How fst will the shoe be moving when it hits the ground? Now plug time into d = v 0 t t2 321 m = 0t (10 m t2 s2) 321 m = 0 + (5 m t2 s2) 321 m (5 m/s 2 ) = (5m/s2 )t 2 (5 m/s 2 ) 64.2 s 2 = t s 2 = t s = t v f = v 0 + t v f = 0 + ((10 m s2) 8.01s) = m/s Known Need to Know v0=0 m/s t=? =g=10.0 m/s 2 vf=? d=321 m d = v 0 t t2 Now I know: t=8.01 sec v f = v 0 + t 2. A bby blue jy sits in tll tree witing the rrivl of its dinner. As the mother lnds on the nest, she drops worm towrd the hungry chick s mouth, but the worm misses nd flls from the nest to the ground in 1.50 s. How high Known Need to Know up is the nest? d = v 0 t + 1 v0=0 m/s vf=? 2 t2 =g=10.0 m/s 2 d=? d = (0 m/s 1.50s) (10 m (1.50s)2 s2) d = (0 ) + 1 (10 m 2 s2) (1.50s)2 Tke it from here: d = (0 ) (10 m s 2) (1.50s)2 = m s 2 s2 t=1.50 s d = v 0 t t m Answer: Height of the nest (3 pts) 3. Chief Boolie is out hunting when coconut flls from tree nd lnds on his toe. If the nut fell for 1.4 s, how fst ws it trveling when it hit Chief Boolie s toe? v = t v = 10 m m s 1.4 s = 14 s2 s 2 14 m/s Answer: Speed of coconut s it hits

10 4. A girffe, who stnds 6.00 m tll, bites brnch off tree to chew on the leves, nd he lets the brnch fll to the ground. How long does it tke the brnch to hit the ground? d = v 0 t t m = (0 m/s t) (10 m (t)2 s2) 6.00 m = 0 + (5 m t2 s2) 6.00 m (5 m/s 2 ) = (5m/s2 )t 2 (5 m/s 2 ) Tke it from here: Known Need to Know v0=0 m/s t=? =g=10.0 m/s 2 d=6.00 m d = v 0 t t m (5 m s 2) = t2 = 1.2 s 2 t 2 = 1.2 s 2 = s 1.10 s Answer: Time for the brnch to rech the ground (3 pts) 5. The Stembot Geyser in Yellowstone Ntionl Prk, Wyoming, is cpble of shooting its hot wter up from the ground with speed of 48.0 m/s. How high cn this geyser shoot? v f = v 0 + t 0 = 48.0 m/s + (10 m s2) t m s = 48.0 m s 48.0 m s + (10 m s2) t 48.0 m (10 m s (10 m = s2) t s 2) (10 m s 2) 4.8s = t Now plug time into d = v 0 t t2 Known v0=-48.0 m/s Remember, the geyser is shooting up; therefore it must hve negtive initil velocity =g=10.0 m/s 2 vf=0 m/s At the top, the highest point, there is no movement; v is zero!!! v f = v 0 + t Now I know: tto the top =4.8 sec Need to Know tto the top=? d=? d = ( 48.0m/s 4.8s) (10 m (4.8s)2 s2) d = ( 230.4m) + (5 m s 2) (23.04s2 ) d = v 0 t t2 d = ( 230.4m) + (115.2m) d = 115m As you might expect, the finl nswer hs negtive displcement. This mens tht the totl distnce the wter hs trveled is mesured up from the ground.

11 6. While repiring defective rdio trnsmitter on the roof of the 442-m-tll Sers Tower in Chicgo, Lyle drops his hmmer, which flls ll the wy to the ground below.. How long will it tke for Lyle s hmmer to fll? t = 2 d t = m 10 m/s 2 = 88.4 s2 = s 9.4 s Answer: time hmmer flls b. With wht speed will the hmmer hit the pvement? v = t v = 10 m m s s = s2 s 2 94 m/s Answer: Speed of hmmer s it hits c. How fr will the hmmer hve fllen fter 1.50 s when jnitor wtches it pss outside n office window? d = v 0 t t2 d = 0 m s 1.5 s m s 2 (1.5 s)2 = 5 m s s2 = m 11.3 m Answer: Distnce from the roof, where the window is 7. In order to open the clm it ctches, segull will drop the clm repetedly onto hrd surfce from high in the ir until the shell crcks. If segull flies to height of 25 m, how long will the clm tke to fll? 2 d t = t = 2 25m 10 m/s 2 = 5 s2 = s 2.2 s Answer: Time of the flling clm

12 8. Billy, mountin got, is rock climbing on his fvorite slope one sunny spring morning when rock comes hurtling towrd him from ledge 40.0 m bove. Billy ducks nd voids injury. d. How fst is the rock trveling when it psses Billy? t = 2 d t = 2 40m 10 m/s 2 = 8 s2 = s v = t v = 10 m m s s = s2 s m/s Answer: Speed of the rock when it psses Billy e. How does this speed compre to tht of cr trveling down the highwy t the speed limit of 25 m/s (equivlent to 55 mi/h)? Slightly fster Answer: Speed of the rock compred to the speed of cr (1 pt) 9. Reverend Northwick climbs to the church belfry one morning to determine the height of the church. From n outside blcony he drops book nd observes tht it tkes 2.00 s to strike the ground below. f. How high is the blcony of the church belfry? d = 0 m s 2s m s 2 (2 s)2 = 5 m s 2 4 s2 = 20 m d = v 0 t t m Answer: Height of blcony g. Why would it be difficult to determine the height of the belfry blcony if the Reverend dropped only one pge out of the book? The pper would flot Answer: Why would single pge not work (1 pt)

13 10. At n musement prk, populr ride known s Free Fll crries pssengers up to height of 33.5 m nd drops them to the ground inside smll cge. How fst re the pssengers going t the bottom of this exhilrting journey? t = 2 d t = m 10 m/s 2 = 6.7 s2 = s v = t v = 10 m m s s = s2 s m/s Answer: Speed t the bottom of the ride 11. A unique type of bsketbll is plyed on the plnet Zrth. During the gme, plyer flies bove the bsket nd drops the bll in from height of 10 m. If the bll tkes 5.0 s to fll, find the ccelertion due to grvity on Zrth. d = 1 2 t2 turns into 2d t 2 = 2 10 m (5 s) 2 = = 8 m s m/s 2 Answer: Accelertion due to grvity on Zrth 12. In the Wizrd of Oz, Dorothy wkens in Munchkinlnd where her house hs been blown by torndo. If the house fell from height of m, with wht speed did it hit the Wicked Witch of the Est when it lnded? t = 2 d t = 2 3,000 m 10 m/s 2 = 600 s2 = s v = t v = 10 m s s = m s s m/s Answer: Speed of house hitting witch

14 13. A Christms tree bll will brek if dropped on hrdwood floor with speed of 2.0 m/s or more. Mrs. Borowski is decorting her Christms tree when her ct, Killer, tps bll, cusing it to fll 15 cm from tree brnch to the floor. [Units!]. How fst does it hit the ground t = 2 d t = m 10 m/s 2 = 0.03 s2 = s v = t v = 10 m m s s = s2 s m/s Answer: speed of impct b. Does the bll brek? No, it won t brek Answer: Does it brek: YES, it breks NO, is does not brek (1 pt) 14. Perhps sometime in the future, NASA will develop progrm to lnd humn being on Mrs. If you were the first Mrs explorer nd discovered tht when you dropped hmmer it took 0.68 s to fll 0.90 m to the ground, wht would you clculte for the grvittionl ccelertion on Mrs? d = 1 2 t2 turns into 2d t 2 = m (0. 68 s) 2 = 1. 8 m s 2 = = m s m/s^2 Answer: grvittionl ccelertion on Mrs