Question

A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate b to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given by(a) $[\frac{\alpha^{2} + \beta^{2}}{\alpha\beta}]t$(b) $[\frac{\alpha^{2} - \beta^{2}}{\alpha\beta}]t$(c) $[\frac{\alpha + \beta}{\alpha\beta}]t$(d) $[\frac{\alpha\beta}{\alpha + \beta}]t$

Answer 1

u=0
t=t1
v=v
a
a
a=, alpha
t1=v/alpha
u=v
v=0
a=beta
t=t2
t2=v/beta
v/alpha+v/beta
v=t(alpha+beta/alpha(beta))