91Ó°ÊÓ

The displacement of an object is defined as the shortest path followed to cover the distance between two points in unit time. The unit of displacement is the same as that of distance.

Given data.

The length of the track is 400 m.

The man completes eight laps around the track.

The total time taken for this motion is 14.5 min.

Now, you know that

$\begin{array}{c}\mathrm{Average}\mathrm{speed}=\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}}\\ \mathrm{Average}\mathrm{velocity}=\frac{\mathrm{Total}\mathrm{displacement}}{\mathrm{Total}\mathrm{time}}\end{array}$

The total distance will be

$\begin{array}{c}\mathrm{d}=8×400\mathrm{m}\\ =3200\mathrm{m}\end{array}$

The person completes eight laps and then comes back to the same position. Then, the displacement is zero because the initial and final points are the same.

Here, is the total time is

$\begin{array}{c}\mathrm{Δ}\mathrm{t}= 14.5 \min \\ = 14.5  × 60 \mathrm{s}\\ = 870 \mathrm{s}\end{array}$

Therefore, substituting the values,

$\begin{array}{c}\mathrm{Average}\mathrm{speed}=\frac{3200\mathrm{m}}{870\mathrm{s}}\\ =3.68\frac{m}{s}\\ \mathrm{Average}\mathrm{velocity}=\frac{0\mathrm{m}}{870\mathrm{s}}\\ =0\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

(a) Hence, the average speed of the person is $3.68\frac{\mathrm{m}}{\mathrm{s}}$.

(b) Hence, the average velocity of the person is 0.