To calculate the acceleration of the car with two washers added to the string, we need to use the given formula for acceleration:
[tex]\[ a = \frac{v_2 - v_1}{t_2 - t_1} \][/tex]
Where:
- [tex]\( v_1 \)[/tex] is the initial velocity
- [tex]\( v_2 \)[/tex] is the final velocity
- [tex]\( t_1 \)[/tex] is the time to travel [tex]\( 0.25 \)[/tex] meters
- [tex]\( t_2 \)[/tex] is the time to travel [tex]\( 0.50 \)[/tex] meters
From the data provided:
- Initial velocity, [tex]\( v_1 = 0.13 \, \text{m/s} \)[/tex]
- Final velocity, [tex]\( v_2 = 0.36 \, \text{m/s} \)[/tex]
- Time to travel [tex]\( 0.25 \)[/tex] meters, [tex]\( t_1 = 2.23 \, \text{s} \)[/tex]
- Time to travel [tex]\( 0.50 \)[/tex] meters, [tex]\( t_2 = 3.13 \, \text{s} \)[/tex]
Using the formula:
[tex]\[
a = \frac{0.36 \, \text{m/s} - 0.13 \, \text{m/s}}{3.13 \, \text{s} - 2.23 \, \text{s}}
\][/tex]
Simplify the values in the numerator and denominator:
[tex]\[
a = \frac{0.23 \, \text{m/s}}{0.90 \, \text{s}}
\][/tex]
Perform the division:
[tex]\[
a \approx 0.25555555555555554 \, \text{m/s}^2
\][/tex]
Therefore, the acceleration of the car with two washers added to the string is approximately [tex]\( 0.2556 \, \text{m/s}^2 \)[/tex].
