A cyclist’s motion is represented on a distance–time graph that is smooth and curved

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

Problem

A cyclist’s motion is represented on a distance–time graph that is smooth and curved. At

t=4\,\text{s}

a tangent is drawn to the curve which passes through the points

(3\,\text{s},15\,\text{m})

and

(5\,\text{s},27\,\text{m})

. The curve itself passes through

(2\,\text{s},7\,\text{m})

and

(6\,\text{s},35\,\text{m})

. Answer the following. (i) Find the instantaneous speed of the cyclist at

t=4\,\text{s}

using the tangent data. (ii) Compute the average speed of the cyclist between

t=2\,\text{s}

and

t=6\,\text{s}

. (iii) Compare the values obtained in parts (i) and (ii) and explain what this indicates about the cyclist’s motion in that interval.