# 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...

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.

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### 1 Answer

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))`

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