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

Hello!

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 $\displaystyle{V}_{{1}}$ for some initial time moment $\displaystyle{t}_{{1}}$ and the speed $\displaystyle{V}_{{2}}$ for some other moment $\displaystyle{t}_{{2}},$ and if we know also that the change of speed was uniform, then this change is the (uniform) acceleration

$\displaystyle{a}=\frac{{{V}_{{2}}-{V}_{{1}}}}{{{t}_{{2}}\ldots}}$

Hello!

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.

$\displaystyle{a}=\frac{{{V}_{{2}}-{V}_{{1}}}}{{{t}_{{2}}-{t}_{{1}}}}.$

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 $\displaystyle{t}_{{2}}-{t}_{{1}}={20}{s},$ $\displaystyle{V}_{{1}}={0}$ (moves from rest) and $\displaystyle{V}_{{2}}={25}\frac{{m}}{{s}},$ so the acceleration, uniform or average, is $\displaystyle\frac{{25}}{{20}}={1.25}{\left(\frac{{m}}{{{s}}^{{2}}}\right)}.$ This is the answer.