Question

An athlete completes one round of a circular track of diameter 200m in 40s. If the continues to run, what will be the distance covered and the displacement at the end of 2 minutes 20 second respectively?

Answer 1

Calculate how many times 2 minutes 20 seconds is of 40 seconds , Multiply that number with circumference of the circular track ,this will be distance travelled. For displacement check the initial and final position of the athlete.

Complete step-by-step answer :
The displacement is the vector quantity. It has magnitude as well as the direction. The distance between the initial and the final position of the object is the displacement of the object.

Distance is the scalar quantity. It is defined as the path covered by the object.
Diameter of the circular track, d=200 m
Radius of the circular track, r=100 m
Time taken to complete one round, t = 40 s
The distance at the end of 2 minutes 20 second can be calculated as:

Time = 2 min 20 sec = 2 (60)+20=140 sec

The number of rounds completed in 140sec is given as:
n=140/40=3.5

So, the distance covered by the athlete is given as:

& \Rightarrow d=3.5\times 2\times 3.14\times 100 \\\ & \Rightarrow d=2200\ \text{m} \\\ \end{aligned}$$ The athlete completes 3.5 rounds in 140 sec. So, the displacement will be zero after each round. The displacement after 0.5 round will be the semi-circular track. Thus, the displacement between the initial and the final position will be the diameter of the track. Therefore displacement is 200 m and the distance covered is 2200m. **Note** : Distance can be related to the total travelled or the total work done, but the displacement is a measure of actual change in position of any object.