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 2.6 Calculating Average Velocity: The Subway Train

Example 2.6 Calculating Average Velocity: The Subway Train

What is the average velocity of the train in part b of Example 2.2, and shown again below, if it takes 5.00 min to make its trip?

The train moves toward the left, from an initial position of 5 point 25 kilometers to a final position of 3 point 75 kilometers.

Figure 2.22

Strategy

Average velocity is displacement divided by time. It will be negative here, since the train moves to the left and has a negative displacement.

Solution

1. Identify the knowns. x_{\mathrm{f}}^{\prime}=3.75 \mathrm{~km}, x_{0}^{\prime}=5.25 \mathrm{~km}, \Delta t=5.00 \mathrm{~min}.

2. Determine displacement, \Delta x^{\prime} '. We found \Delta x ' to be -1.5 \mathrm{~km} in Example 2.2.

3. Solve for average velocity.

\bar{v}=\frac{\Delta x^{\prime}}{\Delta t}=\frac{-1.50 \mathrm{~km}}{5.00 \mathrm{~min}}

4. Convert units.

\bar{v}=\frac{\Delta x^{\prime}}{\Delta t}=\left(\frac{-1.50 \mathrm{~km}}{5.00 \mathrm{~min}}\right)\left(\frac{60 \mathrm{~min}}{1 \mathrm{~h}}\right)=-18.0 \mathrm{~km} / \mathrm{h}

Discussion

The negative velocity indicates motion to the left.