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Two bodies start moving in the same stra...

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 `40ms^-1`, and the second starts from rest with a constant acceleration of `4ms^-2`.Find the time that elapses before the second catches the first body. Find the also the greatest distance between them prior to it and time at which this occurs.

Text Solution

Verified by Experts

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`
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