Question
Show that if a body retards at the rate numerically equal to distance travelled, then the distance travelled by the body before comes to rest is numerically equal to velocity at the time at which the body starts retarding.
Solution
Here we have,
Body retards at a rate of distance travelled.
That is,
a = -s 
Let the velocity of the body when it starts retarding be v0 and come to rest by travelling the distance s.
Integrating both sides of (1) between initial and final limits, 
