A car accelerates from rest at a constant rate `alpha` for some time, after which it decelerates at a constant rate `beta,` to come to rest. If the total time elapsed is t seconds. Then evalute the maximum velocity aquired by the car is

Options

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

Answer

d

Explanation

`t_(1) = v//alpha, t_(2) = v//beta , t =t_(1) + t_(2) = v//alpha + v//beta`
`v = (alphabeta //alpha + beta) t`