Question

If a car decreases in speed to a stop from an initial speed of 21 m/s in a period of 13 s, what is the
average acceleration of the car? Show all work

Answer 1

To calculate the average acceleration of the car, we can use the formula for average acceleration:

\[
a = \frac{{v_f - v_i}}{{t}}
\]

where:
- \(a\) = average acceleration (in m/s²)
- \(v_f\) = final velocity (in m/s)
- \(v_i\) = initial velocity (in m/s)
- \(t\) = time (in seconds)

From the problem:
- The initial speed \(v_i = 21 \, \text{m/s}\)
- The final speed \(v_f = 0 \, \text{m/s}\) (since the car comes to a stop)
- The time period \(t = 13 \, \text{s}\)

Now, we can plug these values into the formula:

\[
a = \frac{{0 \, \text{m/s} - 21 \, \text{m/s}}}{{13 \, \text{s}}}
\]

Calculating the numerator:

\[
0 \, \text{m/s} - 21 \, \text{m/s} = -21 \, \text{m/s}
\]

Now putting that into the equation:

\[
a = \frac{{-21 \, \text{m/s}}}{{13 \, \text{s}}}
\]

Calculating the acceleration:

\[
a \approx -1.6154 \, \text{m/s}^2
\]

Thus, the average acceleration of the car is approximately:

\[
\boxed{-1.62 \, \text{m/s}^2}
\]

(Note: The negative sign indicates that this is a deceleration, as the car is slowing down.)