Two bodies start moving in the same straight line at the same instant of time from the same origin. The first body moves with a constant velocity of 40 m/s, and the second starts from rest with a constant acceleration of `4 "m/s"^2`. Find the time that elapses before the second catches the first body. Find also the greatest distance between then prior to it and the time at which this occurs.

Explanation

When the second body catches the first, the ditance travelled by each is the same.
`40t=1/2(4)t^(2) or t=20S`
Now, the distance s between the two bodies at any time t is
`s=ut-1/2at^(2)`
For s to be maximum.
`(ds)/(dt)=0 or u-at=0`
`or t=u/a=(40)/(4)=10s`
Maximum Distance `=40 xx 10-1/2 xx 4 xx (10)^(2)=400-200=200m`