To determine at which time the horse was traveling the fastest, we need to calculate the speed of the horse over each time interval. Speed can be calculated using the formula:
[tex]\[ \text{Speed} = \frac{\text{Change in Position}}{\text{Change in Time}} \][/tex]
Let's break it down step by step for each interval shown in the table.
1. From 0 s to 1 s:
[tex]\[ \text{Speed} = \frac{\text{Position at 1 s} - \text{Position at 0 s}}{\text{1 s - 0 s}} = \frac{9 - 5}{1 - 0} = \frac{4}{1} = 4 \, \text{m/s} \][/tex]
2. From 1 s to 2 s:
[tex]\[ \text{Speed} = \frac{\text{Position at 2 s} - \text{Position at 1 s}}{\text{2 s - 1 s}} = \frac{13 - 9}{1} = \frac{4}{1} = 4 \, \text{m/s} \][/tex]
3. From 2 s to 3 s:
[tex]\[ \text{Speed} = \frac{\text{Position at 3 s} - \text{Position at 2 s}}{\text{3 s - 2 s}} = \frac{13 - 13}{1} = \frac{0}{1} = 0 \, \text{m/s} \][/tex]
4. From 3 s to 4 s:
[tex]\[ \text{Speed} = \frac{\text{Position at 4 s} - \text{Position at 3 s}}{\text{4 s - 3 s}} = \frac{15 - 13}{1} = \frac{2}{1} = 2 \, \text{m/s} \][/tex]
5. From 4 s to 5 s:
[tex]\[ \text{Speed} = \frac{\text{Position at 5 s} - \text{Position at 4 s}}{\text{5 s - 4 s}} = \frac{20 - 15}{1} = \frac{5}{1} = 5 \, \text{m/s} \][/tex]
Now we have calculated the speeds for each interval:
- Interval from 0 s to 1 s: 4 m/s
- Interval from 1 s to 2 s: 4 m/s
- Interval from 2 s to 3 s: 0 m/s
- Interval from 3 s to 4 s: 2 m/s
- Interval from 4 s to 5 s: 5 m/s
The fastest speed is 5 m/s, which occurs from 4 s to 5 s.
Therefore, the horse was traveling the fastest at 5 s.
