A person jogs eight complete laps around a 400 m track in a total time of 14.5 min. Calculate (a) the average speed and (b) the average velocity in m/s.

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

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

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

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

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.