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

Answer

D

Explanation

`v_("max") = 0 + alpha (t_(1))`
`0-v_("max") - beta (t- t_(1))` …(ii)
Solve both equations, `v_("max") = (alpha beta t)/(alpha + beta)`