A low-friction cart moves along a straight horizontal track

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

Problem

A low-friction cart moves along a straight horizontal track. Its velocity–time representation is described as follows: • The horizontal axis is time

t

(seconds) from

0\,\text{s}

10\,\text{s}

. The vertical axis is velocity

v

(metres per second). • From

t = 0\,\text{s}

t = 4\,\text{s}

, the graph is a horizontal line at

v = +2\,\text{m/s}

. • From

t = 4\,\text{s}

t = 8\,\text{s}

, the graph is a horizontal line at

v = -1\,\text{m/s}

. • From

t = 8\,\text{s}

t = 10\,\text{s}

, the graph is on the time axis (

v = 0

). Answer the following questions about the cart’s motion. (a) Describe, in words, a method for determining the cart’s net displacement between

t = 0\,\text{s}

and

t = 8\,\text{s}

using only the information contained in the graph. (b) Without performing detailed numerical calculations, state whether the cart’s net displacement between

t = 0\,\text{s}

and

t = 10\,\text{s}

is positive, negative, or zero. Clearly explain your reasoning. (c) Explain how the cart’s average velocity for the entire

10\,\text{s}

interval could be obtained from the same graph, and interpret what the sign of that average velocity would indicate about the cart’s overall motion.

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