Question

A runner completes one round of a circular track of diameter 400 m in 40 s. What will be the distance covered and the displacement respectively at the end of 2 minutes 20 s?

• A. 2200 m, 800 m
• B. 4400 m, 400 m
• C. 2200 m, 400 m
• D. 4400 m, 200 m

Answer 1

The correct option is B

4400 m, 400 m

Given:
Diameter of the circle, $d=400m$
Time taken to complete one circle, $T=40s$
Total time of motion, $T_2=2min20s$

Circumference of circle, $C=\pi d$
Speed is defined as the ratio of distance covered to time taken.
Hence, speed of the runner
$v=\frac{C}{T}=\frac{\pi d}{T}$

Total time of motion, $T_2=2min20s=140s$
Total distance covered is given by:
$D=v{T}_2$
$D=\pi d\frac{T_2}{T}$
$D=\pi \times 400\times \frac{140}{40}$
$D\approx 4400m$

No. of rounds completed:
$n=\frac{\text{Total distance covered}}{\text{Circumference of the circle}}$
$n=\frac{D}{\pi d}$
$n=\frac{T_2}{T}$
$n=\frac{1400}{40}=3.5$
This means that he will be at the diametrically opposite end, i.e., he starts at A and ends at B.
Hence displacement, $s=2r=400m$