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
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a
α2+β2αβ
b
α2-β2αβt
c
(α+β)tαβ
d
αβtα+β
answer is D.
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Detailed Solution
In fig., AA1=vmax.=αt1=βt2 But t=t1+t2=vmaxα+vmaxβ=vmax(1α+1β)=vmax(α+βαβ) or, vmax=t(αβα+β)
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