# Q. A body moving with a uniform acceleration and initial speed 'u' covers a distance 'S' in a particular time-interval.Another body moving with initial speed 'v' and same uniform acceleration covers the distance 'S' in double the time.Find the time taken by the first body to cover the distance.

Let us say the acceleration of the object is `am/s^2` and the time is `t` seconds.

Using equations of motion;

`S = ut+1/2at^2`

For the first object;

`S = ut+1/2at^2 ----(1)`

For the second object;

`S = v(2t)+1/2a(2t)^2 `

`S = 2vt+2at^2 ----(2)`

`(2)-(1)xx4`

`S-4S = 2vt-4ut`

`4ut-2vt = 3S`

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Let us say the acceleration of the object is `am/s^2` and the time is `t` seconds.

Using equations of motion;

`S = ut+1/2at^2`

For the first object;

`S = ut+1/2at^2 ----(1)`

For the second object;

`S = v(2t)+1/2a(2t)^2 `

`S = 2vt+2at^2 ----(2)`

`(2)-(1)xx4`

`S-4S = 2vt-4ut`

`4ut-2vt = 3S`

`t = (3S)/(2(2u-v))`

So the time taken for the first body to cover the distance is `(3S)/(2(2u-v))`