Question

1. An athlete completes one round of a circular track of diameter200 m in 40 s. What will be the distance covered and the
displacement at the end of 2 minutes 20 s?
​

Answer 1

An athlete completes one round of a circular track of diameter 200m in 40s.

Given that, the diameter is 200 m. So, the radius is 100 m (half of diameter).

As the athlete covers the path in a circular motion. So, the displacement is zero.

Distance cover in one round (during 40 seconds) = 2πr

(2πr = Circumference of the circle)

→ 2 × 22/7 × 100

→ 4400/7

→ 628.571 m

Distance covered in 1 second (during first or one round) = 628.571/40 = 15.714 m

We have to find the distance covered and the displacement at the end of 2min 20s.

Displacement is zero (as the path is circular). But the athele covers 3.5 rounds (140/40). So, the displacement of the athele is equal to it's diameter of circle i.e. 200 m.

Distance covered in 2min 20sec or 140 sec = 15.714 × 140 = 2199.96 = 2200 m (approx.)

Answer 2

Given :

• An athlete completes one round of a circular track of diameter 200 metre in 40 seconds.

To Find :

• The distance covered and the displacement at the end of 2 minutes 20 second.

Solution :

Here,

Total time = 2 minutes 20 seconds

→ 2 × 60 seconds + 20 seconds

→ 120 seconds + 20 seconds

→ 140 seconds

Now,

In 40 s,the no. of rounds completed = 1

So,

In 140 s,the no. of rounds completed = $\sf\dfrac{1}{40}\times 140$

In 140 s,the no. of rounds completed = 3.5

• Distance covered in 3.5 rounds :

When diameter of the track is 200 m,radius will be 100 m

Now,

[Distance covered in 1 round = Circumference of the circle]

→ 2 × 22/7 × 100

→ 4400/7

→ 628.57

Total Distance covered = 628.57 × 3.5 m

→ 2200

$\therefore$ Distance covered at the end of 2 minutes 20 seconds is 2200 m

• Displacement covered in 3.5 rounds :

The athlete makes three and a half rounds now If the athlete starts from point A,then after completion of 3 rounds he'll be at the point A again. And when again start from point A and makes the remaining half round, he'll reach point B. So,the displacement of athlete will be equal to diameter of the circular track (Point B is diametrically opposite to point A)

$\therefore$ Displacement covered at the end of 2 minutes 20 seconds is 200 m.

Refer to the attachment!