An athlete completes one round of circular track of diameter 50 m in 10 second. What will be the distance cover and the displacement at the end of 45 second?

 An athlete completes one round of circular track of diameter 50 m in 10 second. What will be the distance cover and the displacement at the end of 45 second?

Solution:

Given:

• Diameter of circular track = 50 m
• So radius (r) = 25 m
• Time for 1 round = 10 s
• Total time = 45 s

1) Distance Covered

First, find circumference of the track:

$$\text{Circumference} = 2\pi r = 2\pi (25) = 50\pi \text{ m}$$
$$50\pi \approx 157\text{ m}$$

So, in 10 s → distance = 157 m

In 45 s:

$$\text{Distance}=\frac{157}{10}\times 45\mathrm{<br>}\mathrm{<br>}$$$$= 157 × 4.5$$
$$\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; =706.5\text{ m (approx)}$$

Distance covered ≈ 706.5 m

2) Displacement After 45 Seconds

In 40 seconds → athlete completes 4 full rounds (comes back to starting point).

Remaining time = 5 seconds

In 5 seconds → athlete completes half round.

Half round means he reaches the diametrically opposite point.

Displacement = Diameter of circle

$$=50\text{ m}$$

Displacement = 50 m

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