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 40m//s, and the second starts from rest with a constant acceleration of 4m//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.

Two bodies start moving in the same straight line at the same instant

1.	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 40m//s, and the second starts from rest with a constant acceleration of 4m//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.
Answer» Solution :When the SECOND body catches the first, the DISTANCE travelled by each is the same. `therefore 40T=(1)/(2)(4)t^(2)ort=20S` Now, the distance s between the two bodies at any time t is `s=ut-(1)/(2)at^(2)` For s to be maximum, `(ds)/(dt)=0oru-at=0` or `t=(u)/(a)=(40)/(4)=10S` Maximum Distance `=40xx10-(1)/(2)xx4xx(10)^(2)=400-200=200m`