A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate `beta` to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given by :

Options

A. `((alpha^2+beta^(2))/(alphabeta))t`
B. `((alpha^2- beta^(2))/(alphabeta))t`
C. `((alpha^2- beta)t)/(alphabeta)`
D. `(alpha betat)/(alpha+beta)`

Answer

D

Explanation

`AA_(1) = v_(max)= alphat_(1) = betat_(2)`
But `t = t_(1)+t_(2)=(v_(max))/alpha+(v_max)/beta=v_(max)(1/alpha+1/beta)=v_(max)((alpha+beta)/(alphabeta))`
or `v_(max)((alphabeta)/(alpha+beta))`