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Question

# A car starts from rest and travels with uniform acceleration "α" for some time and then with uniform retardation "β" and comes to rest. The time of motion is "t". Find the maximum velocity attained by it.

A
αβt/(α/2+β)
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B
αβt/(α+β)
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C
αβt/(α+β/2)
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D
α/2βt/(α+β)
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Solution

## The correct option is B αβt/(α+β)let it accelerate for time t1 and retard for time t2t1+t2=t…(1)using v=u+atinitially u=0, vfinal=αt1finally v=0,u=αt10=αt1−βt2t2α=t1β…(2)using (1)&(2)t1=βtα+βmaximum velocity is :αt1vmax=αβtα+β

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