Question

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

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

Answer 1

The correct option is B $4400m,400m$

Radius of the circle, $r=\frac{400}{2}=200m$ Circumference of the circle $=2\pi r$
$=2\times \frac{22}{7}\times 200=\frac{8800}{7}m$
Speed of the runner $=\frac{\left(\frac{8800}{7}\right)}{40}=\frac{220}{7}m{s}^{-1}$
Distance covered in $2\text{min}20s$ i.e. $140s=\frac{220}{7}\times 140=4400m$

Number of rounds completed $=\frac{4400}{\left(\frac{8800}{7}\right)}=3.5$

This means that the person will be at the diametrically opposite end, i.e. starting at A, and ending at B.


Hence, the displacement $=2r=400m$.