ACCELERATION IN ONE DI1\1ENSION Name

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1. A ball rolls up, then down an incline. Sketch an acceleration diagram for the entire motion. (An . acceleration diagram is similar to a velocity diagram; however, thevectors on an acceleration diagram represent the acceleration rather than the velocity of an object.)

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(same instant on uphill and 0. downhill

~ _ figures)

7~7777)7;;;;;777:e7777~:~ Downhill

2. Sketch x versus t, v versus t, and a versus t graphs for the entire motion of a ball rolling up and then d~wn an incline.

a.

b.

x

., \. c.'I

~ .'

Use a coordinate system in which the positive x-direction is down the track.

x v a

Use a coordinate system in which the positive x-direction is up the track. v a

Can an object have a negative acceleration and be speeding up? If so, describe a possible physical situation and a corresponding coordinate system. If not, explain why not.

.Tutorials in lntfoductory P McDermott, Shaffer, & P.E.G., U. Wash.

Mech HW-14

Acceleration in one dimension

Describe the motion of an object:

a. for which the direction of the acceleration is the same as the direction of motion of the object.

b. for which the direction of the acceleration is opposite to the direction of motion of the object.

" c. for w~ich the change in velocity is zero. . ~

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d. for which the initial velocity is zero Qut the aCceleration is riot zero:

4. Two carts roll toward each other on a level table. The vectors represent the velocities of the carts just before and just after they collide. .

A B ~

A B

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I ,a. Draw and label a vector for each cart to representthe change in velocity from before to after the collision. Make the magnitude and direction of your vectors consistent with the vectors I drawn above.

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A~ :: \J,,*- 'IA",

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~,,~..... '~:----------f' -b. How does the direction of the average acceleration of cart A compare to the direction of the

average acceleration of cart B over the time interval shown? Explain.

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·c. For the time interval shown, is tIl~' magnitude of the av.~rage acceleration of cart A greater than, less than, or equal to the magnitude of the average acceleration of cart B? Explain;

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Tutormls in Introductory Physics ©Prehtiee Hall, me. McDermott, Shaffer, & P.E.G., U. Wash. First Editiori,2002

• •

ACCELERATION IN ONE DIMENSION Name Mech

HW-15

5. In this problem, a cart moves in various ways on a horizontal track. A coordinate system with the positive x-direction to the right is used to measure each motion. For each motion, one of five different representations is given: a strobe diagram, a velocity versus time graph, a set of instantaneous velocity vectors, a written description, or a pair of arrows representing the directions of the velocity and acceleration.

Give the remaining four representations for each motion."The first exercise has been worked as an example.

. Given: velocity vectors VI ~ v2 •v3 •- . v4

graph of v vs t top view strobe diagram V

--------­ 1 2 3 cart. • •Jt trade' "

• written description

4 The cart moves in the positive direction and speeds up./'.'

~

arrows

direction of v:.. clirection of a:..

a. Given: The cart moves in the negative direction with constant speed.

velocity vectors graph of v vs tstrobe diagr~ arrows

direction of v:VI ­.4 tt .3 0 \ v2 ­ ~.4 l

cax\ ~ Y§ "\5. I@l v~ v3 4- ; ~. ­ . ,t direct; of a:IJV4 4 track

b. Given: top view strobe diagrarri- 1 2 3 4 cart. iii

track/J

velocity vectors graph of V vs t arrowswritten description, ' "

direction of v:~ UM.t \A ~i'~Vj > 4'N. ~ddl'cl\~ , ~v2 ~ vl ___ t

v3 ~ direction of a: v4 VR%~ opucl ~;-'"

,

arrows

direction of a:

. ----=t.

direction of v:

written description

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'A..:-\o\v...'(V'I.;~ "" '<\.ll\~~y. ~ .

z ;.J

track

~t

strobe diagram .3

velocity vectorS

c., GiYen:grapll ofv vs t v , I

Vj 0.1---­v2 ~4-4__­

v3,,+-' ." v4 -t-

Tutorials in Introductory Physics . ©Prentice Hall,Inc. .McDermott, Shaffer, & P.E.G., U. Wash. First Edition,2002

Mech Acceleration in one dimension HW-16

6. Carts A and B move along a horizontal track. The strobe diagram shows the locations of the carts at instants 1-5, separated by equal time intervals.

1 2 3 4 5 _ • ' • _ • CartA

.1 .1 1 I .. I I

0 CJ 0 0 0 CartBlem 1 2 3 4 5 , a. At instant 3:

• is cart A speeding up, slowing down, or oving with constant sed? Explain. .

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• is cart B eeding up, lowing down, or moving with constant speed? Explain.

t:¥ io. iV\~.~ :"~"'a !O IM~ b. -Is the speed of cart B greater than, le~s than, or equal to the-speed of cart A:

o ",'~, .' ~y- ~c..V\V . •. at instant 2? Explain. vc,."'o'9J ':. '-b ~ -:t: '"~ <.. VA.

. "icN~~:: A.:t..... 4~ . 3? E l' () t b• at lOstant. xp ~n. .

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U -t c., During a small time interval from just before in tant 2 until just 'after instant 2, does th~.

iII: V c. distance between cart A arid cart Bincrease aecrease, or reJn{lin the same? Explain.

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Consider the following response to the above question:

"For the small intervai containing instant 2, cart B is ah~ad and speedingup"so the distance between the carts: must be increasing."

Do you agree or disagree? Explain~ \ .

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d. Is th~e-~yti;;e' inPerval during which cart Aanci c~ B have the same average velocity? If so, identify t,he interval(s) and explain. If not, explain why not. f\.\l. ' J ( ~~l \j,!' {~".' ~~ S";'5~r(.e.. ~ b' ~~

~~,~ tM b.~~ £..Yb " . +k, '.. . Is there any instant at which cart A and cart B have the same instantaneous velocity? If so, identify the instant(s) (e.g., "at instant 1," or "at an instant between 2 and 3") and explain:.. If i·

not, explain why not.. L.....\- __ ~ / "'A"'\... :A ~ J "'~~~ ,,~~ ," ~. <,,~ ~.xeYl1Vy.~·

"~-;Us \ ~ '\fOJ/4t+6ff\j~ I/~" \J6~ >"'A. 60 t ~ Tutorials in Intrqductory Physics ~ 4:~~" _ ©~rentic~!Iall;IUc. McDermott, Shaffer, & P.E.G., U. Wash. ~ A. FlistEditlon,200Z