5. GO The data in the following table describe the initial and final posi- tions of a moving car. The elapsed time for each of the three pairs of po-- sitions listed in the table is 0.50 s. Review the concept of average velocity in Section 2.2 and then determine the average velocity (magnitude and direction) for each of the three pairs. Note that the algebraic sign of your answers will convey the direction. (a) (b) (c) Initial position xo Final position x +2.0 m +6.0 m +6.0 m +2.0 m -3.0 m +7.0 m

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Average Velocity Calculation for a Moving Car

The data in the following table describe the initial and final positions of a moving car. The elapsed time for each of the three pairs of positions listed in the table is 0.50 seconds. Review the concept of average velocity and then determine the average velocity (magnitude and direction) for each of the three pairs. Note that the algebraic sign of your answers will convey the direction.

#### Table of Positions

|   | Initial position \( x_0 \) | Final position \( x \) |
|---|---------------------------|-----------------------|
| (a) | +2.0 m                      | +6.0 m                  |
| (b) | +6.0 m                      | +2.0 m                  |
| (c) | -3.0 m                      | +7.0 m                  |

**Concept Breakdown:**
- **Initial and Final Positions:** The positions are given in meters (m).
- **Elapsed Time:** 0.50 seconds for each pair.
  
**Steps to Calculate Average Velocity:**
1. **Determine Displacement:** For each pair, subtract the initial position \( x_0 \) from the final position \( x \).
2. **Calculate Average Velocity:** Divide the displacement by the elapsed time (0.50 s).

\[ \text{Average Velocity} = \frac{x - x_0}{\text{Elapsed Time}} = \frac{x - x_0}{0.50 \text{ s}} \]

**Note:** The resulting average velocity will indicate direction based on the algebraic sign; a positive sign indicates movement in the positive direction, and a negative sign indicates movement in the negative direction.

### Calculations

1. **Pair (a):**
   - _Initial Position \( x_0 \)_: +2.0 m
   - _Final Position \( x \)_: +6.0 m
   - _Displacement_: \( 6.0 \text{ m} - 2.0 \text{ m} = 4.0 \text{ m} \)
   - _Average Velocity_: \(\frac{4.0 \text{ m}}{0.50 \text{ s}} = 8.0 \text{ m/s} \) (positive direction)

2. **Pair (b):**
   - _Initial Position \( x_0 \)_: +6.
Transcribed Image Text:### Average Velocity Calculation for a Moving Car The data in the following table describe the initial and final positions of a moving car. The elapsed time for each of the three pairs of positions listed in the table is 0.50 seconds. Review the concept of average velocity and then determine the average velocity (magnitude and direction) for each of the three pairs. Note that the algebraic sign of your answers will convey the direction. #### Table of Positions | | Initial position \( x_0 \) | Final position \( x \) | |---|---------------------------|-----------------------| | (a) | +2.0 m | +6.0 m | | (b) | +6.0 m | +2.0 m | | (c) | -3.0 m | +7.0 m | **Concept Breakdown:** - **Initial and Final Positions:** The positions are given in meters (m). - **Elapsed Time:** 0.50 seconds for each pair. **Steps to Calculate Average Velocity:** 1. **Determine Displacement:** For each pair, subtract the initial position \( x_0 \) from the final position \( x \). 2. **Calculate Average Velocity:** Divide the displacement by the elapsed time (0.50 s). \[ \text{Average Velocity} = \frac{x - x_0}{\text{Elapsed Time}} = \frac{x - x_0}{0.50 \text{ s}} \] **Note:** The resulting average velocity will indicate direction based on the algebraic sign; a positive sign indicates movement in the positive direction, and a negative sign indicates movement in the negative direction. ### Calculations 1. **Pair (a):** - _Initial Position \( x_0 \)_: +2.0 m - _Final Position \( x \)_: +6.0 m - _Displacement_: \( 6.0 \text{ m} - 2.0 \text{ m} = 4.0 \text{ m} \) - _Average Velocity_: \(\frac{4.0 \text{ m}}{0.50 \text{ s}} = 8.0 \text{ m/s} \) (positive direction) 2. **Pair (b):** - _Initial Position \( x_0 \)_: +6.
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