Question
A body starts from rest and accelerates uniformly at rate α for time t1 and then retards instantaneously at the rate β for time t2 to come to rest. Show that the ratio of the time of accelerated motion to the time of retarded motion is equal to ratio of retardation to the acceleration.
Solution
For accelerated motion:
Initial velocity, u = 0 m/s
Acceleration =
m/s2
Time taken = t1 sec
Let, v be the velocity acquired by the body at the end of accelerated motion.
By using the relation,
v = u + at,
we have
V = 0 + 
...(1)
For retarded motion, 
Now, using this relation, v= u + at, we have
