To determine the acceleration of the car with two washers added to the string, let's follow a step-by-step approach using the provided data in the table.
1. Identify the given data for two washers:
- Initial velocity [tex]\(v_1\)[/tex] = 0.13 m/s
- Final velocity [tex]\(v_2\)[/tex] = 0.36 m/s
- Time to travel 0.25 m [tex]\(t_1\)[/tex] = 1.92 seconds
- Time to travel 0.50 m [tex]\(t_2\)[/tex] = 2.61 seconds
2. Recall the formula for calculating acceleration:
Acceleration ([tex]\(\alpha\)[/tex]) can be calculated using the formula:
[tex]\[
\alpha = \frac{v_2 - v_1}{t_2 - t_1}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\alpha = \frac{0.36 \, \text{m/s} - 0.13 \, \text{m/s}}{2.61 \, \text{s} - 1.92 \, \text{s}}
\][/tex]
4. Perform the arithmetic operations:
[tex]\[
v_2 - v_1 = 0.36 \, \text{m/s} - 0.13 \, \text{m/s} = 0.23 \, \text{m/s}
\][/tex]
[tex]\[
t_2 - t_1 = 2.61 \, \text{s} - 1.92 \, \text{s} = 0.69 \, \text{s}
\][/tex]
5. Calculate the acceleration:
[tex]\[
\alpha = \frac{0.23 \, \text{m/s}}{0.69 \, \text{s}} = \frac{0.23}{0.69} \approx 0.3333 \, \text{m/s}^2
\][/tex]
6. Conclusion:
Therefore, the acceleration of the car with two washers added to the string is approximately [tex]\( 0.33 \, \text{m/s}^2 \)[/tex].
The completed table will look like this:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline \begin{tabular}{c}
\# of \\
washers
\end{tabular} & \begin{tabular}{c}
Initial \\
velocity \\
$v_1$ \\
$(m / s )$
\end{tabular} & \begin{tabular}{c}
Final \\
velocity \\
$v_2$ \\
$(m / s )$
\end{tabular} & \begin{tabular}{c}
Time to travel \\
0.25 m
\end{tabular} & \begin{tabular}{c}
Time to travel \\
0.50 m
\end{tabular} & Acceleration \\
& 0.11 & 0.28 & $(s)$ & $t_2$ & $\alpha=\left(v_2-v_1\right) /\left(t_2-t_1\right)$ \\
\hline 1 & 0.23 & $(s)$ & 3.13 & 0.19 \\
\hline 2 & 0.13 & 0.36 & 1.92 & 2.61 & 0.333 \\
\hline
\end{tabular}
\][/tex]
