Question

Question 1
An athlete completes one round of a circular track of diameter 200 m in 40 seconds. What will be the distance covered and the displacement at the end of 2 minutes 20 seconds ?

Answer 1

Given, diameter of the circular track, $D=200m$, radius of the circular track, $r=\frac{200}{2}=100m$ and time taken by the athlete in one round, $t=40s$

Distance covered by the athlete in one round, $s=2\pi r$
$=2\times \frac{22}{7}\times 100$
Speed of the athlete, $v=\frac{distance}{time}$
$=\frac{2\times 2200}{7\times 40}$
$=\frac{4400}{7\times 40}$
Therefore, distance covered in 2 minutes 20 s = Speed(s) $\times$ Time (t)
$=\frac{4400}{7\times 40}\times (2\times 60+20)$
$=\frac{4400}{7\times 40}\times 140$
$=2200m$
Number of round in 40 s = 1 round
Number of round in 140 s $=\frac{140}{40}$ $=3.5$
After starting from position X, the athlete will be at position Y after 3.5 rounds as shown in figure.
Hence, displacement of the athlete with respect to initial position = Diameter of the track
$=200m$