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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

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The distance travelled by first body in time `t, s_(1) =40 t`.
The distance travelled by second body in time `t, s_(2) =(1)/(2) xx4xxt^(2) =2t^(1)`
The separation between them at any time `t, s =s_(1)-s_(2) =40 t -2t^(2)`
The second body will catch the first if s = 0
`? 0=40 t -2t^(2)`
which gives t =20 s.
For s to be greatest, `(ds)/(dt) =0`
or `(d)/(dt) (40t-2t^(2)) =0" or "40-2xx2t=0" or "t=10 s`
Thus greatest distance between them `s=40xx10-2xx10^(1)=200 m`
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