A laboratory cart travels along a straight track

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

Problem

A laboratory cart travels along a straight track. Its velocity–time behaviour is represented on a graph described below. • Time axis:

t = 0\text{ s}

t = 9\text{ s}

. • Velocity axis:

v

\text{m/s}

. • From

t = 0\text{ s}

t = 3\text{ s}

, velocity increases linearly from

0\,\text{m/s}

+6\,\text{m/s}

. • From

t = 3\text{ s}

t = 5\text{ s}

, velocity remains constant at

+6\,\text{m/s}

. • From

t = 5\text{ s}

t = 9\text{ s}

, velocity decreases linearly to

-4\,\text{m/s}

t = 9\text{ s}

. Assume motion is confined to a straight line with the

+x

–direction defined as positive velocity. (a) Calculate the cart’s displacement during the interval

0\text{ s} \le t \le 5\text{ s}

. (b) Calculate the cart’s displacement during the interval

5\text{ s} \le t \le 9\text{ s}

. (c) Determine (i) the cart’s total displacement and (ii) the total distance it travels between

t = 0\text{ s}

and

t = 9\text{ s}

. (d) Compute the cart’s average velocity over the entire

9\,\text{s}

interval.