A cart moves along a straight track

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A cart moves along a straight track. Its velocity

v(t)

(in m/s) for

0\le t\le 9

seconds is described by the following verbal graph. •

v(0)=0

and increases linearly to

v(2)=8

. •

v(t)=8

for

2\le t\le 5

. • From

t=5

t=7

v(t)

decreases linearly to

v(7)=-4

. • From

t=7

t=9

v(t)

increases linearly to

v(9)=0

. Assume the motion is along the positive

x

-axis when velocity is positive and along the negative

x

-axis when velocity is negative. (a) Compute the cart’s displacement (change in position) over the time interval

0\le t\le 9

s. (b) Determine the total distance the cart travels during the same interval. (c) Calculate the cart’s average velocity on

0\le t\le 9

s and interpret its meaning in the context of the motion. (d) The track ends

15

meters in the positive direction from the starting point. Does the cart reach the end of the track during the

9

-second interval? Justify your answer mathematically.