To determine which statement best describes the riders' final velocities, we need to calculate the acceleration for each rider based on their time, initial velocity, and final velocity. Acceleration can be calculated using the formula:
[tex]\[ \text{Acceleration} = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Time}} \][/tex]
Let's denote the acceleration of each rider:
1. Gabriella:
- Time: 10 sec
- Initial velocity: 55
- Final velocity: 32
[tex]\[ \text{Acceleration}_{\text{Gabriella}} = \frac{32 - 55}{10} = \frac{-23}{10} = -2.3 \][/tex]
2. Franklin:
- Time: 8.5 sec
- Initial velocity: 50
- Final velocity: 50
[tex]\[ \text{Acceleration}_{\text{Franklin}} = \frac{50 - 50}{8.5} = \frac{0}{8.5} = 0 \][/tex]
3. Kendall:
- Time: 6 sec
- Initial velocity: 53.2
- Final velocity: 67
[tex]\[ \text{Acceleration}_{\text{Kendall}} = \frac{67 - 53.2}{6} = \frac{13.8}{6} \approx 2.3 \][/tex]
Now let's interpret these accelerations:
- Gabriella's acceleration is -2.3. This negative value indicates she is slowing down.
- Franklin's acceleration is 0. This means there is no change in his velocity; he is neither speeding up nor slowing down.
- Kendall's acceleration is approximately 2.3. This positive value indicates he is speeding up.
Given these accelerations, let's evaluate the statements:
1. Gabriella is speeding up at the same rate that Kendall is slowing down, and Franklin is not accelerating.
- This statement is incorrect because Gabriella is slowing down, not speeding up.
2. Gabriella is slowing down at the same rate that Kendall is speeding up, and Franklin is not accelerating.
- This statement is correct. Gabriella is slowing down at a rate of 2.3, Kendall is speeding up at a rate of 2.3, and Franklin is not accelerating (0).
3. Gabriella and Franklin are both slowing down, and Kendall is accelerating.
- This statement is incorrect because Franklin is not slowing down; his acceleration is zero.
4. Gabriella is slowing down, and Kendall and Franklin are accelerating.
- This statement is incorrect because Franklin is not accelerating; his acceleration is zero.
Therefore, the best description of the riders' final velocities is:
Gabriella is slowing down at the same rate that Kendall is speeding up, and Franklin is not accelerating.
