To calculate the acceleration of the car with two washers added to the string, we can use the given data and the formula for acceleration. Here’s a detailed, step-by-step solution:
1. Identify the Relevant Data:
- Initial velocity, \( v_1 = 0.13 \) m/s
- Final velocity, \( v_2 = 0.36 \) m/s
- Time taken to travel \( 0.50 \) meters, \( t_2 = 2.61 \) seconds
- Initial time \( t_1 = 0 \) seconds (assuming the initial measurement starts at \( t_1 = 0 \))
2. Use the Formula for Acceleration:
The formula for acceleration \( a \) is:
[tex]\[
a = \frac{v_2 - v_1}{t_2 - t_1}
\][/tex]
3. Substitute the Values into the Formula:
[tex]\[
a = \frac{0.36 \text{ m/s} - 0.13 \text{ m/s}}{2.61 \text{ s} - 0 \text{ s}}
\][/tex]
4. Simplify the Numerator:
[tex]\[
0.36 \text{ m/s} - 0.13 \text{ m/s} = 0.23 \text{ m/s}
\][/tex]
5. Substitute Back into the Formula:
[tex]\[
a = \frac{0.23 \text{ m/s}}{2.61 \text{ s}}
\][/tex]
6. Calculate the Acceleration:
[tex]\[
a = 0.08812260536398467 \text{ m/s}^2
\][/tex]
Therefore, the acceleration of the car with two washers added to the string would be [tex]\( 0.088 \text{ m/s}^2 \)[/tex] (rounded to three significant figures).
