A runner moves back and forth along a straight

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

Problem

A runner moves back and forth along a straight, one-dimensional track during an

8\,\text{s}

interval. Her position

x

(measured from a fixed origin) is recorded at

2\,\text{s}

intervals, producing the data in the table below.

Time $t$ (s)	Position $x$ (m)
0	$0$
2	$10$
4	$15$
6	$9$
8	$-1$

(a) Calculate the total distance the runner travels between

t=0\,\text{s}

and

t=8\,\text{s}

. (b) Determine the runner’s displacement for the same time interval. (c) Compute the runner’s average speed over the

8\,\text{s}

interval. (d) Compute the runner’s average velocity over the

8\,\text{s}

interval. (e) For each of the four quantities you calculated in parts (a) through (d)—total distance, displacement, average speed, and average velocity—state whether it is a scalar or vector quantity and justify each classification with reference to magnitude and direction.

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