Question
A car accelerates from 0 to 60 km/h in 10 seconds. What is the acceleration of the car?
Answers
GPT-4o mini
To calculate the acceleration of the car, we can use the formula for acceleration:
\[
a = \frac{\Delta v}{\Delta t}
\]
where:
- \( a \) is acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the time taken for that change.
1. Convert the speed from km/h to m/s:
\[
60 \text{ km/h} = \frac{60 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{60000 \text{ m}}{3600 \text{ s}} \approx 16.67 \text{ m/s}
\]
2. The initial velocity (\( v_i \)) is \( 0 \) m/s, and the final velocity (\( v_f \)) is \( 16.67 \) m/s. Therefore, the change in velocity (\( \Delta v \)) is:
\[
\Delta v = v_f - v_i = 16.67 \text{ m/s} - 0 \text{ m/s} = 16.67 \text{ m/s}
\]
3. The time taken (\( \Delta t \)) is 10 seconds.
4. Now, substitute the values into the acceleration formula:
\[
a = \frac{16.67 \text{ m/s}}{10 \text{ s}} = 1.667 \text{ m/s}^2
\]
Therefore, the acceleration of the car is approximately \( 1.67 \text{ m/s}^2 \).
\[
a = \frac{\Delta v}{\Delta t}
\]
where:
- \( a \) is acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the time taken for that change.
1. Convert the speed from km/h to m/s:
\[
60 \text{ km/h} = \frac{60 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{60000 \text{ m}}{3600 \text{ s}} \approx 16.67 \text{ m/s}
\]
2. The initial velocity (\( v_i \)) is \( 0 \) m/s, and the final velocity (\( v_f \)) is \( 16.67 \) m/s. Therefore, the change in velocity (\( \Delta v \)) is:
\[
\Delta v = v_f - v_i = 16.67 \text{ m/s} - 0 \text{ m/s} = 16.67 \text{ m/s}
\]
3. The time taken (\( \Delta t \)) is 10 seconds.
4. Now, substitute the values into the acceleration formula:
\[
a = \frac{16.67 \text{ m/s}}{10 \text{ s}} = 1.667 \text{ m/s}^2
\]
Therefore, the acceleration of the car is approximately \( 1.67 \text{ m/s}^2 \).