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Question

A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

A
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C
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D
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Solution

The correct option is D

Let the car accelerate at rate α for time t1 then maximum velocity attained , v=0+αt1=αt1

Now,the car decelerates at a rate βfor time (tt1) and finally comes to rest.Then,

0=vβ(tt1)0=αt1βt+βt1
t1=βα+βt
v=αβα+βt


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