Question

An athlete completes 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

Step 1: Given

The diameter of the circular track = 200 m

Radius (r) = 200/2 = 100 m

Time is taken by an athlete to complete one round(t) = 40 seconds.

Total time athlete moves(T) = 2 min 20 seconds

T = 2 min 20 seconds = 2 × 60 + 20

T= 2 min 20 seconds = 140 seconds

Step 2: Formula used

Speed = Distance/Time

Step 3: Finding the distance covered in one round

Distance covered in one round = Circumference of a circle.

Distance covered in one round = 2πr

Distance covered in one round = 2 × 100 × π

Distance covered in one round = 200π

Time is taken by an athlete to complete one round = 40 seconds.

Step 4: Find the distance covered in 140 s

Number of rounds completed in 140 s = $\frac{140}{40}$

Number of rounds completed in 140 s = 3.5

Distance covered = 3.5 × circumference

Distance covered = 3.5 × 2πr

Distance covered = 3.5 × 2 × 3.14 × 100

Distance covered = 2198 ≈ 2200 m

Step 5: Find the displacement covered in 140 s

An athlete completes 3.5 rounds of the ground.

For complete 3-round displacement is 0 m.

For the remaining 0.5 round displacement = Diameter of the ground = 200 m(shortest distance is displacement).

Hence, distance and displacement at the end of 2 minutes 20 s are 2200 m and 200 m respectively.