Question
a car moving at 15m's comes to a stop in 10 seconds. what is its acceleration
Answers
GPT-4o mini
To find the acceleration of the car, you can use the formula for acceleration:
\[
a = \frac{{v_f - v_i}}{t}
\]
Where:
- \( a \) = acceleration (in meters per second squared, m/s²)
- \( v_f \) = final velocity (in meters per second, m/s)
- \( v_i \) = initial velocity (in meters per second, m/s)
- \( t \) = time (in seconds, s)
In this case:
- The initial velocity \( v_i = 15 \, \text{m/s} \) (the speed of the car before stopping)
- The final velocity \( v_f = 0 \, \text{m/s} \) (the car comes to a stop)
- The time \( t = 10 \, \text{s} \)
Plugging in these values, we get:
\[
a = \frac{{0 \, \text{m/s} - 15 \, \text{m/s}}}{10 \, \text{s}} = \frac{{-15 \, \text{m/s}}}{10 \, \text{s}} = -1.5 \, \text{m/s}^2
\]
The negative sign indicates that the acceleration is in the opposite direction to the car's initial motion (deceleration). Thus, the acceleration of the car is:
\[
-1.5 \, \text{m/s}^2
\]
\[
a = \frac{{v_f - v_i}}{t}
\]
Where:
- \( a \) = acceleration (in meters per second squared, m/s²)
- \( v_f \) = final velocity (in meters per second, m/s)
- \( v_i \) = initial velocity (in meters per second, m/s)
- \( t \) = time (in seconds, s)
In this case:
- The initial velocity \( v_i = 15 \, \text{m/s} \) (the speed of the car before stopping)
- The final velocity \( v_f = 0 \, \text{m/s} \) (the car comes to a stop)
- The time \( t = 10 \, \text{s} \)
Plugging in these values, we get:
\[
a = \frac{{0 \, \text{m/s} - 15 \, \text{m/s}}}{10 \, \text{s}} = \frac{{-15 \, \text{m/s}}}{10 \, \text{s}} = -1.5 \, \text{m/s}^2
\]
The negative sign indicates that the acceleration is in the opposite direction to the car's initial motion (deceleration). Thus, the acceleration of the car is:
\[
-1.5 \, \text{m/s}^2
\]