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Question

When a body repeats its motion in regular interval of time then it's said to execute periodic motion. Let's say a car is going on a race track (as shown in figure)

The car covers 5 laps.

For each lap it took 10 mins

In which of the below mentioned cases will its motion be considered periodic.

Case I: The car was travelling with constant speed.

Case II: The car had a constant acceleration from rest (0 m/s) and then a constant deceleration to rest (0 m/s) in each lap for all 5 laps.

Case III: The car had a non-uniform acceleration throughout the journey.

Case IV: lap 1 with constant speed, lap 2 with constant acceleration, lap 3, 4, 5 with variable acceleration.

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Solution

The correct option is **B**

Case II is periodic

You know that a motion that repeats itself in equal intervals of time is called periodic, right?

Let's discuss what it means exactly,

It means that after some specific interval of time T the position of the body from the reference point and its velocity become equal to what they were at the reference point. so no matter

what reference point you choose in the path, after time T the motion "repeats” itself.

In case I and II if we choose any reference point in the path we find after passing of time equivalent to a multiple of T=10 min the motion "repeats” itself.

This wouldn't happen for case III and IV.

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