Question

A car moves along a circular road of radius 200/π m with a constant speed of 36 kmph starting at a time t=0. Then the minimum time after which the magnitude of change in velocity is half of the maximum change in velocity is
A. 20/3 sec
B. 40/3 sec
C. 20 sec
D. 80/3 sec

Answer 1

I think that the question is trying to ask at what time can we get the max change in velocity.

Answer 2

Answer:

$\frac{20}{3} sec$

Explanation:

Magnitude of Change in velocity will be the maximum when velocities (at two instants) are oppositely directed. If the car performs uniform circular motion with speed v, we'll have,

Magnitude of maximum change in velocity = $2V$

Also,

Magnitude of change in velocity till the instant the car makes an angular displacement $\theta$ = $2V[sin(\frac{\theta}{2})]$

Now let's search for the instant (or angular displacement) when the modulus of change in velocity is half of the modulus of maximum change in velocity

i. e.,

or  $sin(\frac{\theta}{2}) = \frac{1}{2}$

⇒ $\theta = \frac{\pi}{3}$    [For minimum time interval]

Now write this angular displacement in terms of linear distance (or arc covered).

Arc covered = = =

∴ Time taken = The distance covered by the arc / Speed

                       $= \frac{200/3}{10}seconds$

                       $= \frac{20}{3}seconds$

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