Accelerated Motion Worksheet Answers PDF

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Accelerated Motion Worksheet Answers...

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Name Date

Pd

Uni f or ml yAccel er at edPar t i cl eModelWor ksheet4:

I nt er pr et i ngGr aphsofAccel er at edMot i on

positon

Obj e c tA:

B A

C D

tme G

E F

a .Wh e r eont hegr a pha bo v ei st h eob j e c tmo vi n gmo s ts l o wl y ?Ho wdoy oukno w? Theob j e c ti sno tmo vi n ga tl oc a t i onsBa ndF.Wekn o wt hi sb e c a us et hes l opeoft h et a n g e n t i sz e r o( i not he rwo r d st hec u r v ei sho r i z ont a la tt hos epoi nt s ) .I ft hes t ude nti n t e r pr e t st he q u e s t i ont ome a nwhe r ei si ta c t ua l l ymo vi n gbuta tt hes l o we s tr a t e , t hel o c a t i on swo ul dbej us t b e f o r ea nda f t e rBa ndF .Re a s o ni n gi st ha tt hes l op ei sv e r ys ma l l . b .Be t we e nwh i c hpo i nt si st h eob j e c ts pe e d i n gup?Ho wdoy oukn o w? Theob j e c ti ss p e e di n gupbe t we e nBa ndCa n da l s obe t we e nFa ndG.Wekn o wt hi sbe c a us e b e t we e nt ho s epo i nt st h es l opei sc o nt i n ua l l yi nc r e a s i n gi ns t e e p ne s s .

c . Be t we e nwhi c hpoi nt si st heob j e c ts l o wi n gdo wn?Ho wdoy oukn o w? Theob j e c ti ss l o wi n gdo wnbe t we e nAa n dBa nda l s obe t we e nEa ndF .( a n da l s oa f t e rG)We kno wt hi sbe c a us ebe t we e nt h os ep oi n t st h es l o pei sc o nt i n ua l l yd e c r e a s i n gi ns t e e pne s s .

d .Wh e r eont hegr a pha bo v ei st h eob j e c tc h a n gi n gdi r e c t i on?Ho wdoy oukno w? Theob j e c ti sc h a n gi n gdi r e c t i ona tBa ndF.Wekn o wt h i sbe c a us et hes l o pei sg oi n gf r om n e g a t i v et opos i t i v eorpo s i t i v et on e g a t i v ea tt he s epoi nt s .

©Modeling Instruction - AMTA 2013

1

U3 Uniform acceleration - ws 4 v3.0

25

position (m)

20

15

10

5

0 0

time (s)

5

10

a .Gi v eawr i t t e nde s c r i p t i onoft hemo t i on. Ob j e c tBi ss t a r t i n gf r omr e s ta tt he25 mpos i t i o na nds p e e di n gupi nt h ene g a t i v ed i r e c t i on. b .Re pr e s e ntob j e c tB’ smo t i onwi t hamo t i onma p.I nc l ud ebo t hv e l o c i t ya nda c c e l e r a t i onv e c t or s . vel: v

v

v

v

0m a

a

a

a

+

acc: c . Fi ndt h edi s pl ac e me ntf r o m t=2. 0st ot=8. 0s .  x At8st h epos i t i oni s9ma nda t2si ti s24 m. xf  xi 9.0m  24.0m  15.0m d .Fi ndt hea v e r a g ev e l oc i t yf r omt=2. 0st ot=8. 0s . v 

x  15.0m   2.5 ms  t 8.0s  2.0s

e . Fi ndt hei ns t ant ane o usv e l o c i t ya tt=2. 0sa ndt=8 . 0 sb yfindi n gs l o pe soft a n g e nt s . Tofindt h es l op eoft het a n g e ntIwi l lfindt hes l opeoft hes e c a ntwhe r et h emi d t i me sa r e2a nd8s .  x 21.0m  25.0m  x 0.0m  16.0m v 2s  v8s    1.0 ms   4.0 ms 4.0s  0.0s 10.0 s  6.0 s t t f .De t e r mi net hea v e r ag eac c e l e r a t i onf r o m t=2. 0st ot=8. 0s . v  4.0 ms  ( 1.0 ms ) a   0.50 ms2 8.0s  2.0s t g .Wh a ti st hei ns t ant ane o usv e l o c i t ya tt=5. 0s ?Expl a i n.

©Modeling Instruction - AMTA 2013

2

U3 Uniform acceleration - ws 4 v3.0

I nd .wef o undt hea v e r a g ev e l oc i t yf o rt hei nt e r v a lof2st o8 s .Th emi d t i meo ft hi si nt e r v a li s 5 s .Th e r e f o r et hea v e r a g ea ndi n s t a nt a ne ousa r et hes a mev a l ueof2 . 5ms .

©Modeling Instruction - AMTA 2013

3

U3 Uniform acceleration - ws 4 v3.0

Obj e c tC: 9 6 ( 3 v s ( 0 ( m/ s) ) m 3 6 / 6 s ) 9

2

4

6

t ( s )

a .Gi v eawr i t t e nde s c r i p t i onoft hemo t i on. Att i met=0ob j e c tCi st r a v e l i n gi nt h ene g a t i v edi r e c t i ona t3m/ s .I tt h e ns p e e dsupf o rt he n e x t8s e c ond s . b .Sk e t c hamo t i o nma p.Bes ur et oi nc l ud ebo t hv e l oc i t ya nda c c e l e r a t i o nv e c t or s . vel:

v

v

v

v

0m

acc:

a

a

a

+a

c . De t e r mi net hedi s p l a c e me ntf r o mt=0 st ot=4s . Us i n gt hea r e ao ft her e ds e c t i onoft hegr a ph :  3.0 ms (4.0 s) r e c t a n g l ei s 3.0 ms (4.0s )  12.0m p l ust r i a n gl e  6.0 m = −18.0m. 2  3.0 ms  (  6.0 ms ) h  h2 v v i a sat r a pe z oi d:Atrap  x  1 t  w f (4.0s )  18.0m 2 2 2 d .De t e r mi net hedi s pl a c e me ntf r o m t=4st ot=8s . Us i n gt hea r e ao ft hegr e e ns e c t i o noft hegr a ph:  3.0 ms (4.0 s) r e c t a n g l ei s 6.0 ms (4.0s )  24.0m p l ust r i a n gl e  6.0 m =−30.0m. 2  6.0 ms  (  9.0 ms ) h  h2 v v i a sat r a pe z oi d:Atrap  x  1 t  w f (4.0s )  30.0m 2 2 2 e . De t e r mi net hea v e r a g ea c c e l e r a t i ono ft heob j e c t ’ smo t i o n. m m v  9.0 s  ( 3.0 s ) a   0.75 sm2 8.0s  0.0s t x f .Sk e t c hapo s s i bl ex tgr a p hf ort hemo t i o noft heob j e c t . m) Ex pl a i nwh yy ou rgr a p hi son l yon eofma n ypos s i bl egr a p hs .( Weh a v enoi d e awhe r et hei ni t i a lpo s i t i onf o rt het r i pi s .

©Modeling Instruction - AMTA 2013

4

t( s)

U3 Uniform acceleration - ws 4 v3.0

Obj e c tD: 8 6 4 2 v ( m/ s) 0 2 4

4

2

6

t ( s )

6 8 a .Gi v eawr i t t e nde s c r i p t i onoft hemo t i on. Ob j e c tDi st r a v e l i n gi nt hene g a t i v edi r e c t i o na t4m/ s .Att i met=2si tb e gi nst os l o wdo wn a ndi n s t a n t a ne ou s l ys t ops2sl a t e r .I tt he ns p e e d su pi nt hepos i t i v edi r e c t i onf or4s .

b .Sk e t c hamo t i o nma p.Bes ur et oi nc l ud ebo t hv e l oc i t ya nda c c e l e r a t i o nv e c t or s . vel:

v

v

v

v

v

v

start v

v end

0m

acc:

a

a a

a a

a

a

+ a

a

c . De t e r mi net hedi s p l a c e me ntf r o mt=0 st ot=4s . Us i n gt hea r e ao ft her e ds e c t i onoft hegr a ph :  4.0 ms (2.0 s) ust r i a n g l e r e c t a n g l ei s 4.0 ms (2.0s )  8.0m pl  4.0 m = −12.0m. 2 d .De t e r mi net hedi s pl a c e me ntf r o m t=4st ot=8s . Us i n gt hea r e ao ft hegr e e ns e c t i o noft hegr a ph: m 8.0 (4.0s ) 16.0m Tr i a n gl e : s 2 e . De t e r mi net hedi s p l a c e me ntf r omt=2st ot=6s . Byi n s p e c t i onon ec a ns e et ha tt het r i a n g l ei nt h ene g a t i v es e c t i onha st hes a mea r e aa st he t r i a n gl ei nt hepo s i t i v es e c t i on.Th e r e f or et h edi s p l a c e me nti sz e r o ,

f .De t e r mi net heob j e c t ’ sa c c e l e r a t i ona tt=4s . x ( m)

 v 8.0 ms  (  4.0 ms )  2.0 sm2 a 8.0s  2.0s t

t( s)

g .Sk e t c hap os s i bl ex tgr a phf ort hemo t i o noft heob j e c t . Ex pl a i nwh yy ou rgr a p hi son l yon eofma n ypos s i bl egr a p hs . Weh a v enoi d e awhe r et hei ni t i a lpo s i t i onf o rt het r i pi s . ©Modeling Instruction - AMTA 2013

5

U3 Uniform acceleration - ws 4 v3.0

©Modeling Instruction - AMTA 2013

6

U3 Uniform acceleration - ws 4 v3.0...