Question
A car begins from a standstill and reaches a velocity of 42 m/s after 7.0 seconds. What is the average acceleration of the car?
Answers
GPT-4o mini
To calculate the average acceleration of the car, we can use the formula for average acceleration:
\[
a_{\text{avg}} = \frac{\Delta v}{\Delta t}
\]
where:
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the change in time.
In this case:
- The initial velocity \( v_0 = 0 \) m/s (since the car starts from a standstill),
- The final velocity \( v = 42 \) m/s,
- The time interval \( \Delta t = 7.0 \) s.
First, we calculate the change in velocity:
\[
\Delta v = v - v_0 = 42 \, \text{m/s} - 0 \, \text{m/s} = 42 \, \text{m/s}
\]
Now, we can substitute the values into the acceleration formula:
\[
a_{\text{avg}} = \frac{42 \, \text{m/s}}{7.0 \, \text{s}} = 6 \, \text{m/s}^2
\]
Therefore, the average acceleration of the car is \( 6 \, \text{m/s}^2 \).
\[
a_{\text{avg}} = \frac{\Delta v}{\Delta t}
\]
where:
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the change in time.
In this case:
- The initial velocity \( v_0 = 0 \) m/s (since the car starts from a standstill),
- The final velocity \( v = 42 \) m/s,
- The time interval \( \Delta t = 7.0 \) s.
First, we calculate the change in velocity:
\[
\Delta v = v - v_0 = 42 \, \text{m/s} - 0 \, \text{m/s} = 42 \, \text{m/s}
\]
Now, we can substitute the values into the acceleration formula:
\[
a_{\text{avg}} = \frac{42 \, \text{m/s}}{7.0 \, \text{s}} = 6 \, \text{m/s}^2
\]
Therefore, the average acceleration of the car is \( 6 \, \text{m/s}^2 \).