To solve this problem, we need to determine the average velocity of the car over two separate segments, each 0.25 meters long. Here’s the step-by-step breakdown:
### Step 1: Determine Average Times
We have two sets of trial times for each 0.25-meter segment. Let's first find the average time for each set.
#### For the first 0.25 meters:
The times recorded are:
- Trial \#1: 2.24 seconds
- Trial \#2: 2.21 seconds
- Trial \#3: 2.23 seconds
To find the average time ([tex]\( t_1 Avg \)[/tex]) for the first 0.25 meters:
[tex]\[
t_1 Avg = \frac{(2.24 + 2.21 + 2.23)}{3} = \frac{6.68}{3} \approx 2.2267 \text{ seconds}
\][/tex]
#### For the second 0.25 meters:
The times recorded are:
- Trial \#1: 3.16 seconds
- Trial \#2: 3.08 seconds
- Trial \#3: 3.15 seconds
To find the average time ([tex]\( t_2 Avg \)[/tex]) for the second 0.25 meters:
[tex]\[
t_2 Avg = \frac{(3.16 + 3.08 + 3.15)}{3} = \frac{9.39}{3} = 3.13 \text{ seconds}
\][/tex]
### Step 2: Calculate Average Velocities
To find the average velocity, we use the formula:
[tex]\[
\text{Velocity} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
For both segments, the distance covered is 0.25 meters.
#### Average velocity for the first 0.25 meters:
[tex]\[
\text{Velocity}_{t1} = \frac{0.25 \text{ m}}{2.2267 \text{ s}} \approx 0.1123 \text{ m/s}
\][/tex]
#### Average velocity for the second 0.25 meters:
[tex]\[
\text{Velocity}_{t2} = \frac{0.25 \text{ m}}{3.13 \text{ s}} \approx 0.0799 \text{ m/s}
\][/tex]
### Summary of Results
- The average velocity of the car over the first 0.25 meters is approximately [tex]\(0.1123 \text{ m/s}\)[/tex].
- The average velocity of the car over the second 0.25 meters is approximately [tex]\(0.0799 \text{ m/s}\)[/tex].
