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

Answer 1

The correct option is B

4400 m, 400 m

Radius of the circle, $r=200m$

Circumference of the circle $=2\pi r$

$=2\times \frac{22}{7}\times 200=\frac{8800}{7}m$

Speed of the runner $=\frac{\left(\frac{8800}{7}\right)}{40}=\frac{220}{7}m/s$

Distance covered in 2 min 20 s i.e. $140s=\frac{220}{7}\times 140$

$=4400m$

No. of rounds completed $=\frac{4400}{\left(\frac{8800}{7}\right)}=3.5$ rounds

This means he will be at the diametrically opposite end, i.e., he starts at A and ends at B.

Hence displacement $=2r=400m$