To find the acceleration of the car with two washers added to the string, we can use the given information about the initial and final velocities as well as the times taken to travel specific distances.
The formula for acceleration [tex]\( a \)[/tex] when you know the initial velocity [tex]\( v_1 \)[/tex], final velocity [tex]\( v_2 \)[/tex], the initial time [tex]\( t_1 \)[/tex], and the final time [tex]\( t_2 \)[/tex] is:
[tex]\[ a = \frac{v_2 - v_1}{t_2 - t_1} \][/tex]
Given values:
- Initial velocity ([tex]\( v_1 \)[/tex]): [tex]\(0.13 \, \text{m/s}\)[/tex]
- Final velocity ([tex]\( v_2 \)[/tex]): [tex]\(0.36 \, \text{m/s}\)[/tex]
- Time to travel [tex]\(0.25 \, \text{m}\)[/tex] ([tex]\( t_1 \)[/tex]): [tex]\(1.92 \, \text{s}\)[/tex]
- Time to travel [tex]\(0.50 \, \text{m}\)[/tex] ([tex]\( t_2 \)[/tex]): [tex]\(2.61 \, \text{s}\)[/tex]
Now, we substitute these values into the acceleration formula:
[tex]\[ a = \frac{0.36 \, \text{m/s} - 0.13 \, \text{m/s}}{2.61 \, \text{s} - 1.92 \, \text{s}} \][/tex]
[tex]\[ a = \frac{0.23 \, \text{m/s}}{0.69 \, \text{s}} \][/tex]
After performing the division:
[tex]\[ a \approx 0.333333 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration of the car with two washers added to the string is approximately [tex]\( 0.333 \, \text{m/s}^2 \)[/tex].
