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 $2\min 20\mathrm{s}?$

Answer 1

Solve using speed distance relation :

Step 1: Find the distance covered by the athlete in one round.

Given diameter of the circular track is $200\mathrm{m}$.

Know that the circumference of a circle $=\pi \times$diameter

Find the distance covered in $40$ seconds.

$\begin{array}{l}=200\times \pi \\ =200\times \frac{22}{7}\mathrm{m}\left[\because \pi =\frac{22}{7}\right]\end{array}$

Step 2: Find the speed of the athlete

Speed $\begin{array}{rcl}& =& \frac{\mathrm{distance}}{\mathrm{time}}\end{array}$

$\begin{array}{rcl}& =& \frac{200\times {\displaystyle \frac{22}{7}}}{40}\\ & =& \frac{110}{7}\mathrm{m}/\mathrm{s}\end{array}$

Step 3:Find the distance covered in $2\min 20\mathrm{s}$:

We know that, $2\min 20\mathrm{s}=140\mathrm{s}$

Distance $\begin{array}{rcl}& =& \mathrm{speed}\times \mathrm{time}\end{array}$

$\begin{array}{rcl}& =& \frac{110}{7}\times 140\\ & =& 2200\mathrm{m}\end{array}$

Understand that : $2200\mathrm{m}=2.2\mathrm{km}$.

Step 4: Find the displacement.

We know that the displacement of the athlete after every complete lap is $0$.

We know that the athlete completes a single round in $40\mathrm{s}$. Therefore in$140\mathrm{s}$, in the first $120\mathrm{s}$ he will cover $3$complete rounds and then he will cover some more distance in remaining $20\mathrm{s}$.

Since, in $40\mathrm{s}$ he completes one round of the circular track. Therefore, in $20\mathrm{s}$ he will complete half round of the circular track.

Understand that, when he completes half round his position is exactly opposite to the starting point.

Hence, the displacement at the end of $2\min 20\mathrm{s}$ is equal to the diameter of the circular track i.e., $200\mathrm{m}$.

Hence the distance and the displacement at the end of $2\min 20\mathrm{s}$is $2.2\mathrm{km}$ and $200\mathrm{m}$ respectively.