A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t , then maximum velocity acquired by the car is given by

Let the car accelerates for a time f, and travels a distance s1 . Suppose the maximum velocity attained by the car be v. Thens1=12at2  and  v=αt2,t1=v/α∴s1=12×α×V2α2=V22α....(i)Let the car decelerates for a time t2 and travels a distances s2 .Thens2=vt2−12βt22 and 0=v−βt2or t2=Vβ∴s2=v×vβ−12βv2β2or s2=v2β−v22β=v22β.....(ii)Now, t1+t2=t  or  Vα+Vβ=t∴V=11α+1β=αβα+βtand S = S1 + S2=V22α+V22β=V221α+1β