Calculating Acceleration: A Subway Train Speeding Up

It is worth it at this point to make a simple sketch:

Figure 2.19

This problem involves three steps. First we must determine the change in velocity, then we must determine the change in time, and finally we use these values to calculate the acceleration.

1. Identify the knowns. $v_0=0$ (the trains starts at rest), $v_{\mathrm{f}}=\text{30}\text{.}\text{0 km/h}$, and $\mathrm{\Delta }t=\text{20}\text{.}\text{0 s}$.

2. Calculate $\mathrm{\Delta }v$. Since the train starts from rest, its change in velocity is $\mathrm{\Delta }v\text{=}\text{+}\text{30.0 km/h}$, where the plus sign means velocity to the right.

3. Plug in known values and solve for the unknown, $\stackrel{-}{a}$.

4. Since the units are mixed (we have both hours and seconds for time), we need to convert everything into SI units of meters and seconds. (See Physical Quantities and Units for more guidance.)

The plus sign means that acceleration is to the right. This is reasonable because the train starts from rest and ends up with a velocity to the right (also positive). So acceleration is in the same direction as the change in velocity, as is always the case.