Question

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

Answer 1

Given :

Diameter of circular track = 200 m

Radius 'r' = 200/2 = 100 m

To find :

Time taken by the athlete to complete one round of circular track = 40 seconds

Now,

Time = 2 min 20s = 2 × 60 + 20 = 140 seconds

(Since, 1 minute = 60 seconds)

Number of rounds covered by the athlete = Total time / Time taken to complete one round

= 140/40 = 3.5

Formula :

Circumference of a circle = 2πr

Let's Do that :

Distance covered in 1 round = Circumference of the circular track

Thus, circumference of the circular track = 2 × 22/7 × 100

Distance traveled in 140 seconds = Number of rounds covered × Circumference of the track

= 3.5 × 2 × 22/7 × 100

= 0.5 × 2 × 22 × 100

Thus, Distance covered = 2200m

Now, to calculate the displacement let's look into the below diagram.

Let the athlete start from point A and reach point B after 140s

Thus, the displacement will be equal to the length of the line segment AB

Length of AB = Diameter of the circle = 200m

★ Thus, Displacement of the athlete is 220m

Therefore, the distance covered by the athlete to complete a circular track of a diameter 200m at the end of 2 min 20 seconds is 2200m or 22km and displacement is 200 m.

Answer 2

Given

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

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To Find

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

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Solution

Diameter of track → 200 m

Radius of track → Diameter ÷ 2

Radius of track → 200 ÷ 2 = 100 m

Time taken to complete 1 round → 40 s

Time → 2 min 20 s = 120 + 20 = 140 s

Number of rounds to be covered in 140 sec → $\dfrac{140}{40} = 3.5$

∴ The athlete would complete 3.5 rounds in 140 seconds (2 minutes 20 seconds)

Distance covered by the athlete in 140 sec → 3.5 × Circumference of track

Distance covered → 3.5 × 2 × 22/7 × 100

Distance covered → 200 × 22/2

Distance covered → 100 × 22

Distance covered → 2200

∴ The total distance covered in 2 minutes and 20 seconds (140 s) is 2200 m.

At the end of 3.5 rounds, the athlete would reach the other end of the field so the displacement would be equal to the diameter.

∴ Displacement covered at the end of 2 minutes 20 seconds (140 s) would be 200 m.

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