Calculating Displacement: A Subway Train

A drawing with a coordinate system is already provided, so we don’t need to make a sketch, but we should analyze it to make sure we understand what it is showing. Pay particular attention to the coordinate system. To find displacement, we use the equation $\mathrm{\Delta }x=x_{\mathrm{f}}-x_0$. This is straightforward since the initial and final positions are given.

1. Identify the knowns. In the figure we see that $x_{\mathrm{f}}=\text{6.70 km}$ and $x_0=\text{4.70 km}$ for part (a), and ${x\prime }_{\mathrm{f}}=3\text{.75 km}$ and ${x\prime }_0=5\text{.25 km}$ for part (b).

2. Solve for displacement in part (a).

3. Solve for displacement in part (b).

The direction of the motion in (a) is to the right and therefore its displacement has a positive sign, whereas motion in (b) is to the left and thus has a negative sign.