If displacement is 72.1 m, initial velocity is zero and time is 0.735 s, find the acceleration.

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Probably a body moves with a uniform acceleration, denote it `a.` Then the speed changes uniformly, `V(t) = V_0 + a t,` where `V_0` is the initial speed and `t` is the time in seconds since the initial moment. Because the initial speed is given to be zero, we have `V(t) = a t.`

Therefore the displacement from the initial position is equal to `D(t) = (a t^2) / 2` (proving this requires integration or computing the area of a triangle but I hope you know this fact).

The unknown in our problem is `a,` to find it we multiply both sides of the equation `(a t^2) / 2` by `2` and divide by `t^2` and obtain the answer  `a = (2 D) / t^2.`

Numerically it is equal to  `(2 * 72.1) / 0.735^2 approx 267 (m / s^2).`

 

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