Question

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

Answer 1

Hint: We will first find the length of track using the diameter given. Then, we will find out the velocity of the athlete with the time given to complete one round of the track. Then from the time given, we will find out the final position of the athlete and that will help us to find the distance and displacement.

Complete step by step solution:

Let us assume that initially the athlete is at point A on the track.
Now, according to the question, the radius of the circular track, R = 100m.
Therefore, total length of the track $=2\pi R=200\pi$
 Now, it is given that the time taken to complete one round of the circular track by the athlete = 40s.
Thus, the speed of the athlete $={\displaystyle \frac{200\pi }{40}}=5\pi$ m/s.
Therefore, in 2 min 20s or 140s, the distance travelled by the athlete will be $=5\pi \times 140=700\pi$ m.
Thus, on completion of the journey, the athlete will be covering three rounds of the circular track and $100\pi$m i.e. half of the track length and will reach at a point diametrically opposite to the point B.
We know that the displacement of an object is the shortest distance between the initial and final positions.
Thus, here the shortest distance between the points A and B will be the same as that of the diameter, 200m.
Hence, distance covered will be $700\pi$m and displacement will be 200m.

Note: There can be a mistake that one may take the displacement as the semi-perimeter of the track. We can also find the final location of the athlete by finding the number of rounds the athlete can make by dividing the time given by the time taken in one revolution.