College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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## Understanding Velocity-Time Graphs for Motorcycles

### Graph Description

The figure illustrates a velocity-versus-time (v\_x vs t) graph for a motorcycle moving along the x-axis. The graph provides a visual representation of how the motorcycle's velocity changes over time.

- **Y-Axis (v\_x)**: Represents the velocity of the motorcycle in meters per second (m/s).
- **X-Axis (t)**: Represents the time elapsed in seconds (s).

### Graph Analysis

1. **Initial Velocity**: At time t = 0 seconds, the velocity (v\_x) of the motorcycle is 8 m/s.
2. **Constant Velocity**: From t = 0 to t = 6 seconds, the motorcycle maintains a constant velocity of 8 m/s. This is depicted by the horizontal line on the graph.
3. **Deceleration Phase**: From t = 6 seconds to t = 8 seconds, the velocity decreases linearly from 8 m/s to 0 m/s. The line segment sloping downward indicates this deceleration.

### Calculating Average Acceleration

To determine the average acceleration of the motorcycle during the time interval from t = 0 to t = 8 seconds, use the formula for average acceleration:

\[ a_{avg} = \frac{\Delta v}{\Delta t} \]

Where:
- \(\Delta v\) represents the change in velocity.
- \(\Delta t\) represents the change in time.

Given:
- Initial velocity (v\_i) = 8 m/s
- Final velocity (v\_f) = 0 m/s (at t = 8 s)
- Initial time (t\_i) = 0 s
- Final time (t\_f) = 8 s

\[ \Delta v = v_f - v_i = 0 \, \text{m/s} - 8 \, \text{m/s} = -8 \, \text{m/s} \]

\[ \Delta t = t_f - t_i = 8 \, \text{s} - 0 \, \text{s} = 8 \, \text{s} \]

Now, calculating the average acceleration:

\[ a_{avg} = \frac{-8 \, \text{m/s}}{8 \, \text{s}} = -1 \, \
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Transcribed Image Text:## Understanding Velocity-Time Graphs for Motorcycles ### Graph Description The figure illustrates a velocity-versus-time (v\_x vs t) graph for a motorcycle moving along the x-axis. The graph provides a visual representation of how the motorcycle's velocity changes over time. - **Y-Axis (v\_x)**: Represents the velocity of the motorcycle in meters per second (m/s). - **X-Axis (t)**: Represents the time elapsed in seconds (s). ### Graph Analysis 1. **Initial Velocity**: At time t = 0 seconds, the velocity (v\_x) of the motorcycle is 8 m/s. 2. **Constant Velocity**: From t = 0 to t = 6 seconds, the motorcycle maintains a constant velocity of 8 m/s. This is depicted by the horizontal line on the graph. 3. **Deceleration Phase**: From t = 6 seconds to t = 8 seconds, the velocity decreases linearly from 8 m/s to 0 m/s. The line segment sloping downward indicates this deceleration. ### Calculating Average Acceleration To determine the average acceleration of the motorcycle during the time interval from t = 0 to t = 8 seconds, use the formula for average acceleration: \[ a_{avg} = \frac{\Delta v}{\Delta t} \] Where: - \(\Delta v\) represents the change in velocity. - \(\Delta t\) represents the change in time. Given: - Initial velocity (v\_i) = 8 m/s - Final velocity (v\_f) = 0 m/s (at t = 8 s) - Initial time (t\_i) = 0 s - Final time (t\_f) = 8 s \[ \Delta v = v_f - v_i = 0 \, \text{m/s} - 8 \, \text{m/s} = -8 \, \text{m/s} \] \[ \Delta t = t_f - t_i = 8 \, \text{s} - 0 \, \text{s} = 8 \, \text{s} \] Now, calculating the average acceleration: \[ a_{avg} = \frac{-8 \, \text{m/s}}{8 \, \text{s}} = -1 \, \
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