Acceleration
Read this text. Pay attention to the examples which show how to solve equations of motion. These include how to calculate displacement, given average velocity and time, and how to calculate final velocity, given initial velocity, acceleration, and time.
Example 2.2 Calculating Displacement: A Subway Train
Example 2.2 Calculating Displacement: A Subway Train
What are the magnitude and sign of displacements for the motions of the subway train shown in parts (a) and (b) of Figure 2.18?
Strategy
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 \(\Delta x=x_{\mathrm{f}}-x_{0}\). This is straightforward since the initial and final positions are given.
Solution
- Identify the knowns. In the figure we see that \(x_{\mathrm{f}}=6.70 \mathrm{~km}\) and \(x_{0}=4.70 \mathrm{~km}\) for part (a), and \(x_{\mathrm{f}}^{\prime}=3.75 \mathrm{~km}\) and \(x_{0}^{\prime}=5.25 \mathrm{~km}\) for part (b).
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Solve for displacement in part (a).
\(\Delta x=x_{\mathrm{f}}-x_{0}=6.70 \mathrm{~km}-4.70 \mathrm{~km}=+2.00 \mathrm{~km}\)
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Solve for displacement in part (b).
\(\Delta x^{\prime}=x_{\mathrm{f}}^{\prime}-x_{0}^{\prime}=3.75 \mathrm{~km}-5.25 \mathrm{~km}=-1.50 \mathrm{~km}\)
Discussion
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.