Question

A car with an initial velocity of 16.0 meters per second east slows uniformly to 6.0 meters per second east in 4.0 seconds. What is the acceleration of the car during this 4.0-second interval?

Answer 1

To find the acceleration of the car, we can use the formula for acceleration, which is given by:

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

where:
- \( a \) is the acceleration,
- \( v_f \) is the final velocity,
- \( v_i \) is the initial velocity, and
- \( t \) is the time interval.

Given:
- Initial velocity (\( v_i \)) = 16.0 m/s (east)
- Final velocity (\( v_f \)) = 6.0 m/s (east)
- Time interval (\( t \)) = 4.0 s

Now we can plug in the values:

\[
a = \frac{{6.0 \, \text{m/s} - 16.0 \, \text{m/s}}}{{4.0 \, \text{s}}}
\]

Calculating the numerator:

\[
6.0 \, \text{m/s} - 16.0 \, \text{m/s} = -10.0 \, \text{m/s}
\]

Now, substituting back into the formula:

\[
a = \frac{{-10.0 \, \text{m/s}}}{{4.0 \, \text{s}}} = -2.5 \, \text{m/s}^2
\]

Thus, the acceleration of the car during the 4.0-second interval is:

\[
\boxed{-2.5 \, \text{m/s}^2}
\]

This negative value indicates that the car is decelerating (slowing down) in the eastward direction.