# An athlete completes one round of a circular track of diameter 200 m in 40 s.

Question.
An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s ?

Solution:
Given

Diameter of circular track, $2 \mathrm{r}=200 \mathrm{~m}$

Circumference of circular track $=2 \pi \mathrm{r}$

$s=\pi(2 r)=\frac{22}{7} \times 200=\frac{4400}{7} \mathrm{~m}$

Time for completing one round $=40 \mathrm{~s}$.

Time for which the athlete ran $=2 \mathrm{~min}$ and $20 \mathrm{~s}=140 \mathrm{~s}$

Now distance covered by the athlete in $40 \mathrm{~s}$ is

$\mathrm{s}=\frac{4400}{7} \mathrm{~m} \therefore$ Distance covered in $1 \ \mathrm{~s}=\frac{4400}{7 \times 40} \mathrm{~m}$

(i) Therefore, distance covered by athlete in $140 \mathrm{~s}$

$\mathrm{s}=\frac{4400}{7} \mathrm{~m} \therefore$ Distance covered in $1 \mathrm{~s}=\frac{4400}{7 \times 40} \mathrm{~m}$

(ii) As the athlete returns to the initial point in $40 \mathrm{~s}$, his displacement $=0$

Now,

Number of rounds in 40 seconds $=1$

Hence number of rounds in $140 \mathrm{~s}$ is $=\frac{140}{40}=3 \frac{1}{2}$.

For each complete round the displacement is zero.

Therefore for 3 complete rounds, the displacement will be zero.

Thus, his displacement $=$ diameter of circular track $=200 \mathrm{~m}$

$\therefore$ Displacement after $140 \mathrm{~s}=200 \mathrm{~m}$