Question

an athlete completes one round of a circular track of diameter 200 m in 30 s. find the distance travelled by him, and magnitude of the displacement at the end of 3 min 20 sec​

Answer 1

Answer:

Answer: The distance covered by the athlete is 2200 m and the displacement at the end of 2 min 20s is 200 m.

Let's understand the given problem.

Explanation:

Given : Diameter of circular track = 200 m

Radius 'r' = 200/2 = 100 m

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

Circumference of a circle = 2πr 

Distance covered in 1 round = Circumference of the circular track

Thus, the 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, the distance covered by the athlete is = 2200 m

Now, to calculate the displacement let's observe the following diagram.

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

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

Length of AB = Diameter of the circle = 200 m

Thus, the displacement of the athlete is 200 m

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

Answer 2

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Answer: The distance covered by the athlete is 2200 m and the displacement at the end of 2 min 20s is 200 m.

Let's understand the given problem.

Explanation:

Given : Diameter of circular track = 200 m

Radius 'r' = 200/2 = 100 m

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

Circumference of a circle = 2πr  

Distance covered in 1 round = Circumference of the circular track

Thus, the 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, the distance covered by the athlete is = 2200 m

Now, to calculate the displacement let's observe the following diagram.

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

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

Length of AB = Diameter of the circle = 200 m

Thus, the displacement of the athlete is 200 m

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

Explanation: