A car at rest accelerates at a constant rate `alpha` for sometime after which it decelerates at a constant rate `beta` to come ot rest . If the total time elapsed is t second find the maximum velocity attained.

Explanation

If `t_(1)` is the time taken to reach the maximum velocity v,
v = 0+`at_(1)" ""or",t_(1)=(v)/(a)`
After decelerating if the car takes time `t_(2)` to come to rest
`0 = v -betat_(2)" ""or",t_(2)=(v)/(beta)`
So,`t=t_(1)+t_(2)=(v)/(a)+(v)/(beta)=v(a+beta)/(abeta)`
`:. v = (abeta)/(a+beta)t`