Certainly! Let's break down the problem step-by-step to find the car's acceleration.
1. Identify the given information:
- The car starts from rest. This means the initial velocity ([tex]\(u\)[/tex]) is [tex]\(0 \, m/s\)[/tex].
- The final velocity ([tex]\(v\)[/tex]) after 10 seconds is [tex]\(40 \, m/s\)[/tex].
- The time duration ([tex]\(t\)[/tex]) is [tex]\(10\)[/tex] seconds.
2. Recall the formula for acceleration:
Acceleration ([tex]\(a\)[/tex]) is defined as the change in velocity divided by the time over which the change occurs. The formula is:
[tex]\[
a = \frac{v - u}{t}
\][/tex]
where:
- [tex]\(a\)[/tex] is the acceleration.
- [tex]\(v\)[/tex] is the final velocity.
- [tex]\(u\)[/tex] is the initial velocity.
- [tex]\(t\)[/tex] is the time taken.
3. Substitute the known values into the formula:
[tex]\[
a = \frac{40 \, m/s - 0 \, m/s}{10 \, s}
\][/tex]
4. Perform the calculations:
[tex]\[
a = \frac{40 \, m/s}{10 \, s} = 4 \, m/s^2
\][/tex]
5. Conclusion:
Therefore, the car's acceleration is [tex]\(4 \, m/s^2\)[/tex].
The correct answer is [tex]\(\boxed{4 \, m/s^2}\)[/tex].
