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

Explanation

`u=0`, let in acceleration for `t_1` s and decelerate for `t_2`s so that total time `t= v_(1)+t_(2)`. Velocity acquired by the car after `t_1`s is v, `v= u+a_(1)t_(1), t_(1)= v"/"a_(1)`.
After `t_2`s velocity v becomes zero. `0= v-a_(2)t_(2), t_(2)= v"/"a_(2), t= (v"/"a_(1)) +(v"/"a_(2)), v= a_(1)a_(2) t"/"a_(1)+a_(2)`.