A train moves from rest to a speed of 25 m/s in 20 seconds. What is its acceleration?  

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Borys Shumyatskiy eNotes educator | Certified Educator

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Acceleration is the measure of the changing speed of a body over time, in the same manner as speed is the measure of the changing position of a body.

If we know the speed `V_1` for some initial time moment `t_1` and the speed `V_2` for some other moment `t_2,` and if we know also that the change of speed was uniform, then this change is the (uniform) acceleration

`a = (V_2 - V_1)/(t_2 - t_1).`

If we don't know that the change was uniform, then this formula gives us the average acceleration. Note that only a difference between times is required, so we may set a reference point for time anywhere.

For this problem, we know `t_2-t_1 = 20 s,` `V_1 = 0` (moves from rest) and `V_2 = 25 m/s,` so the acceleration, uniform or average, is  `25/20 = 1.25 (m/s^2).` This is the answer.

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