\begin{tabular}{|c|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Number of \\
washers
\end{tabular} & Trial & \begin{tabular}{l}
Time
\end{tabular} & \begin{tabular}{l}
0.25 m
\end{tabular} & [tex]$t_2(s)$[/tex] & \begin{tabular}{l}
10.50 m
\end{tabular} \\
\hline
\multirow{3}{}{\begin{tabular}{l}
1 washer mass = \\
4.9 g
\end{tabular}} & Trial \#1 & 2.24 & \multirow{3}{
}{\begin{tabular}{l}
Average \\
2.23
\end{tabular}} & 3.16 & \multirow{3}{*}{\begin{tabular}{l}
Average \\
3.13
\end{tabular}} \\
\cline{2-3} \cline{5-5}
& Trial \#2 & 2.21 & & 3.08 & \\
\cline{2-3} \cline{5-5}
& Trial \#3 & 2.23 & & 3.15 & \\
\hline
\end{tabular}

What is the average velocity of the car over the first 0.25 m? [tex]$\square$[/tex] [tex]$m/s$[/tex]

What is the average velocity of the car over the second 0.25 m? [tex]$\square$[/tex] [tex]$m/s$[/tex]



Answer :

Let's break down the solution step-by-step to find the average velocity of the car over the first and second [tex]\(0.25 \, \text{m}\)[/tex].

### Step 1: Identify the given data

For the first [tex]\(0.25 \, \text{m}\)[/tex]:
- Time for Trial 1: [tex]\( 2.24 \, \text{s} \)[/tex]
- Time for Trial 2: [tex]\( 2.21 \, \text{s} \)[/tex]
- Time for Trial 3: [tex]\( 2.23 \, \text{s} \)[/tex]
- Given average time: [tex]\( 2.23 \, \text{s} \)[/tex]

For the second [tex]\(0.25 \, \text{m}\)[/tex]:
- Time for Trial 1: [tex]\( 3.16 \, \text{s} \)[/tex]
- Time for Trial 2: [tex]\( 3.08 \, \text{s} \)[/tex]
- Time for Trial 3: [tex]\( 3.15 \, \text{s} \)[/tex]
- Given average time: [tex]\( 3.13 \, \text{s} \)[/tex]

### Step 2: Calculate the distance
The distance for both sections is [tex]\(0.25 \, \text{m}\)[/tex].

### Step 3: Average velocity formula
The average velocity [tex]\( v \)[/tex] can be calculated using the formula:
[tex]\[ v = \frac{d}{t} \][/tex]
where
- [tex]\( d \)[/tex] is the distance
- [tex]\( t \)[/tex] is the time

### Step 4: Calculate the average velocity for the first [tex]\(0.25 \, \text{m}\)[/tex]
[tex]\[ v_1 = \frac{0.25 \, \text{m}}{2.23 \, \text{s}} \][/tex]
[tex]\[ v_1 \approx 0.11210762331838565 \, \text{m/s} \][/tex]

### Step 5: Calculate the average velocity for the second [tex]\(0.25 \, \text{m}\)[/tex]
[tex]\[ v_2 = \frac{0.25 \, \text{m}}{3.13 \, \text{s}} \][/tex]
[tex]\[ v_2 \approx 0.07987220447284345 \, \text{m/s} \][/tex]

### Conclusion

1. The average velocity of the car over the first [tex]\(0.25 \, \text{m}\)[/tex] is approximately [tex]\( 0.112 \, \text{m/s} \)[/tex].
2. The average velocity of the car over the second [tex]\(0.25 \, \text{m}\)[/tex] is approximately [tex]\( 0.080 \, \text{m/s} \)[/tex].

Therefore:

- The average velocity over the first [tex]\(0.25 \, \text{m}\)[/tex] is [tex]\( 0.112 \, \text{m/s} \)[/tex].
- The average velocity over the second [tex]\(0.25 \, \text{m}\)[/tex] is [tex]\( 0.080 \, \text{m/s} \)[/tex].