To find the acceleration of the car with two washers added to the string, we will use the following given data:
- 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
The formula to calculate acceleration [tex]\( a \)[/tex] is given by:
[tex]\[
a = \frac{v_2 - v_1}{t_2 - t_1}
\][/tex]
Now, substitute the values into the formula:
[tex]\[
a = \frac{0.36 \text{ m/s} - 0.13 \text{ m/s}}{2.61 \text{ s} - 1.92 \text{ s}}
\][/tex]
Calculate the numerator (change in velocity):
[tex]\[
0.36 \text{ m/s} - 0.13 \text{ m/s} = 0.23 \text{ m/s}
\][/tex]
Calculate the denominator (change in time):
[tex]\[
2.61 \text{ s} - 1.92 \text{ s} = 0.69 \text{ s}
\][/tex]
Now, divide the change in velocity by the change in time:
[tex]\[
a = \frac{0.23 \text{ m/s}}{0.69 \text{ s}} \approx 0.3333 \text{ m/s}^2
\][/tex]
Thus, the acceleration of the car with two washers added to the string is approximately 0.3333 m/s².
