please help me solve this problem in kinematics:?

Question

A particle starting from rest moves with constat acceleration 'a' and attains a velocity 'v' , then moves with uniform velocity 'v' for certain time and then decelerates at a constant rate 'b'. if 't' is the total time of motion, find the value of 'v' (in terms of a & b),so that 't' is minimum.

Answer 1

I assume you want t as a minimum to get a certain distance. But, this question doesn't really make any sense.

You want a & b to be infinite to minimize t.

Answer 2

V ^b SQRT b*T=D