Question
A car accelerates from 0 to 60 mph in 10 seconds. What is its acceleration?
Answers
GPT-4o mini
To calculate the acceleration of the car, we can use the formula for acceleration, which is defined as the change in velocity divided by the time taken for that change. The formula is:
\[
a = \frac{\Delta v}{\Delta t}
\]
Where:
- \( a \) is the acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the time taken for the change.
1. First, convert the velocity from miles per hour (mph) to meters per second (m/s) since acceleration is typically expressed in meters per second squared (m/s²).
\[
60 \text{ mph} = 60 \times \frac{1609.34 \text{ meters}}{3600 \text{ seconds}} \approx 26.82 \text{ m/s}
\]
2. The initial velocity (\( v_i \)) is 0 m/s (the car starts from rest), and the final velocity (\( v_f \)) is approximately 26.82 m/s.
3. The change in velocity (\( \Delta v \)) is:
\[
\Delta v = v_f - v_i = 26.82 \text{ m/s} - 0 \text{ m/s} = 26.82 \text{ m/s}
\]
4. The time taken (\( \Delta t \)) is 10 seconds.
5. Now, we can calculate the acceleration:
\[
a = \frac{\Delta v}{\Delta t} = \frac{26.82 \text{ m/s}}{10 \text{ s}} = 2.682 \text{ m/s}^2
\]
Thus, the acceleration of the car is approximately \( 2.68 \, \text{m/s}^2 \).
\[
a = \frac{\Delta v}{\Delta t}
\]
Where:
- \( a \) is the acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the time taken for the change.
1. First, convert the velocity from miles per hour (mph) to meters per second (m/s) since acceleration is typically expressed in meters per second squared (m/s²).
\[
60 \text{ mph} = 60 \times \frac{1609.34 \text{ meters}}{3600 \text{ seconds}} \approx 26.82 \text{ m/s}
\]
2. The initial velocity (\( v_i \)) is 0 m/s (the car starts from rest), and the final velocity (\( v_f \)) is approximately 26.82 m/s.
3. The change in velocity (\( \Delta v \)) is:
\[
\Delta v = v_f - v_i = 26.82 \text{ m/s} - 0 \text{ m/s} = 26.82 \text{ m/s}
\]
4. The time taken (\( \Delta t \)) is 10 seconds.
5. Now, we can calculate the acceleration:
\[
a = \frac{\Delta v}{\Delta t} = \frac{26.82 \text{ m/s}}{10 \text{ s}} = 2.682 \text{ m/s}^2
\]
Thus, the acceleration of the car is approximately \( 2.68 \, \text{m/s}^2 \).