Question

An athlete completes one round of a circular track of diameter $200\mathrm{m}$ in $40\mathrm{s}$. What will be the distance covered and the displacement at the end of $2minutes20s?$

Answer 1

Step 1: Given data,

The diameter of the circular track $=200m$

Radius $r=\frac{200}{2}=100m$

Time taken by an athlete to complete one round $=40s$.

Total time for which the athlete moves $=2min20seconds=(2\times 60)+20=140s$

Step 2: Calculate the distance and displacement,

We know, $Speed=\frac{Dis\tan ce}{Time}$

Distance covered in one round = The Circumference of a circle.

Distance covered in one round $=2\pi r=2\times 100\times \pi =200\pi$

As the athlete takes $40s$ to complete one round.

So, the number of rounds completed in $140s=\frac{140}{40}=3.5$

So, the distance covered in $140s=3.5\times circumference$

$$\begin{gathered} =3.5\times 200\mathrm{\pi } \\ \Rightarrow 3.5\times \frac{22}{7}\times 200=2200\mathrm{m} \end{gathered}$$

Now during 3 revolutions, the displacement is zero, since the athlete has reached the starting point.
Therefore, actual displacement is due to half revolution = Diameter of circular track $=200\mathrm{m}$

Thus, the distance covered in the give case is $2200m$ and the displacement is $200m$.