A car accelerates from rest at a constant rate αfor some time after  which it decelerates at a constant rate βto come to rest.  If the total time elapsed is “t” then the maximum velocity attained is

from A to B:initial velocity =0;final velocity=V;acceleration =α; time=t1 substitute in V=u+at,---(1) V   =    α  t1   ⇒    t1   =    Vα---(2) from B to C:initial velocity =V;final velocity=0;acceleration =-β;time=t2 substitute in equation(1) 0=V-βt2⇒   t2   =    Vβ---(3) add equations (2) and (3)  t1  +    t2   =    t Vα   +   Vβ   =      t⇒      V   =    α β tα+β