Question

An athlete complets 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?

Answer 1

Given that,

Diameter $D=200m$

Radius $r=100m$

Time, complete one round $t=40s$

Time in 2 minute 20 second $t=2\times 60+20$

We know that,

Circumference of circle $=2\pi r=2\times 3.14\times 100=628m$

Now, in 40 s athlete cover a distance of 628 m

In 1 s distance covered by the athlete $=\frac{628}{40}=15.7$

In 140 s distance covered by the athlete $=15.7\times 140=2198m$

Now, the number of rounds

$n=\frac{2198}{628}$

$n=3.5$

So, in given time of $2$ minute $20$ second, athlete will complete $3.5$ rounds to the circular track

Now, $3.5$ rounds means three rounds and half round. This means after the $3.5$ rounds athlete will be just opposite to the starting point that means the displacement is equal to the diameter of circular path

Hence, the distance covered is $2198m$ and displacement is $200m$