To find the acceleration of the car with two washers, we need to use the given data in the table and apply the formula for acceleration. Let's follow these steps carefully:
1. Identify the given values:
- 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 s
- Time to travel 0.50 m ([tex]\(t_2\)[/tex]): 2.61 s
2. Recall the formula for acceleration:
[tex]\[
a = \frac{v_2 - v_1}{t_2 - t_1}
\][/tex]
3. Plug in the values to the formula:
[tex]\[
a = \frac{0.36 \text{ m/s} - 0.13 \text{ m/s}}{2.61 \text{ s} - 1.92 \text{ s}}
\][/tex]
4. Calculate the differences:
[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. Divide the velocity difference by the time difference to find the acceleration:
[tex]\[
a = \frac{0.23 \text{ m/s}}{0.69 \text{ s}} \approx 0.333 \text{ m/s}^2
\][/tex]
Therefore, the acceleration of the car with two washers added to the string is approximately 0.333 m/s².
