An athlete completes one round of a circular track of diameter 100 m in 20 s. What will be the displacements after 1 minute and 10 s, respectively ?

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Q: 6 (CDS-II/2021)
An athlete completes one round of a circular track of diameter 100 m in 20 s. What will be the displacements after 1 minute and 10 s, respectively ?

question_subject: 

Maths

question_exam: 

CDS-II

stats: 

0,24,30,13,9,8,24

The correct answer is option 4: 0 m, 100 m.

To understand this, we need to consider the definition of displacement. Displacement refers to the distance between the initial and final positions of an object, in a straight line. It does not take into account the actual path taken by the object.

In this question, the athlete completes one round of a circular track with a diameter of 100 m in 20 seconds. Since the track is a circle, the distance travelled in one round is equal to the circumference of the track. The circumference of a circle is given by the formula C = πd, where d is the diameter. Therefore, in one round, the athlete covers a distance of 100π meters.

Now, if the athlete were to complete one round in 20 seconds, we can calculate the speed as distance/time = 100π/20 = 5π m/s.

To find the displacement after 1 minute and 10 seconds (70 seconds), we need to calculate how many rounds the athlete completes in that time. Since the athlete completes one round in 20 seconds, in 70 seconds, the athlete completes 70/20 = 3.5 rounds.

Now, let`s calculate the displacements:

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