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Question

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


A

2200m,200m

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B

2200m,0m

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C

4400m,400m

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D

2200m,400m

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Solution

The correct option is A

2200m,200m


Explanation for the correct option:

Step 1: Given data in the question.

In the question, it is given that, An athlete completes one round of a circular track of diameter 200m in 4s.

Step 2: Concept and formula to be used.

  1. The length of the circumference l of the circle when the diameter d is given can be calculated as follows: l=πd
  2. When the distance D and time T is given then the speed S can be calculated as follows: S=DT
  3. According to the definition of displacement, displacement is defined as the shortest distance between the initial point and the final point.
  4. When the time T of completing one round and the time t at which the number of rounds to be calculated is given. Then the number of rounds n can be given by: n=tT.

Step 3: Find the required distance and displacement.

Find the length l of the circumference of the track.

l=π·200l=628.31

That means the athlete completes one round of the track of length 628.31m in 40s.

So, the speed s of the athlete is given as follows:

s=628.3140s=15.70

Therefore, the speed of the athlete is 15.70m/s.

Now, find the distance d travelled by the athlete in 2 minutes 20s.

Since, 2 minutes 20s is equal to 140s.

So, d=15.70·140d=2198

This means that the athlete travelled approximately 2200m in 2 minutes 20s.

Find the number of rounds n the athlete completes in 2 minutes 20s.

n=14040n=3.5

since, the athlete completes three and a half rounds in 2 minutes 20s.

So, at the end of 2 minutes 20s athlete is on the diametrically opposite side from the starting point.

So, the displacement of the athlete at the end of 2 minutes 20s is 200m.

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

Hence, option A is the correct answer.


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