Sure! Let's work through this problem step-by-step.
### Given Data
- Initial velocity, \( v_1 = 0.13 \, \text{m/s} \)
- Final velocity, \( v_2 = 0.36 \, \text{m/s} \)
- Time for the car to travel \( 0.25 \, \text{m} \), \( t_1 = 1.92 \, \text{s} \)
### Step-by-Step Solution
1. Calculate the acceleration:
The formula to calculate acceleration is:
[tex]\[
a = \frac{{v_2 - v_1}}{{t_1}}
\][/tex]
- Substitute the given values:
[tex]\[
a = \frac{{0.36 \, \text{m/s} - 0.13 \, \text{m/s}}}{1.92 \, \text{s}}
\][/tex]
2. Simplify the expression to find acceleration:
- Calculate the difference in velocity:
[tex]\[
0.36 \, \text{m/s} - 0.13 \, \text{m/s} = 0.23 \, \text{m/s}
\][/tex]
- Divide by the time:
[tex]\[
\frac{0.23 \, \text{m/s}}{1.92 \, \text{s}} = 0.11979166666666666 \, \text{m/s}^2
\][/tex]
So, the acceleration of the car is:
[tex]\[
a = 0.11979166666666666 \, \text{m/s}^2
\][/tex]
2. Predict the new acceleration if the force is cut in half:
The acceleration is directly proportional to the force (from Newton's Second Law: \( F = ma \)). If the force is halved, the acceleration will also be halved. Therefore:
[tex]\[
a_{\text{new}} = \frac{a}{2} = \frac{0.11979166666666666 \, \text{m/s}^2}{2} = 0.05989583333333333 \, \text{m/s}^2
\][/tex]
### Final Responses
- The acceleration of the car with the given data is:
[tex]\[
0.11979166666666666 \, \text{m/s}^2
\][/tex]
- If the applied force were cut in half, the new acceleration would be:
[tex]\[
0.05989583333333333 \, \text{m/s}^2
\][/tex]
