A car is coasting backwards downhill at a speed of 3.2 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 5.0 m/s. Assuming that the uphill is the positive direction, what is the car's average acceleration?
Divide the velocity change, (5.0 -(-3.2)) = 8.2 m/s, by the time interval (2.5 s).
The answer will have dimensions of m/s^2
Note the sign change in the velocity.
To find the car's average acceleration, we need to use the formula:
average acceleration = (final velocity - initial velocity) / time
In this case, the final velocity is 5.0 m/s (moving uphill), the initial velocity is -3.2 m/s (coasting backwards downhill), and the time is 2.5 s.
Substituting the values into the formula, we get:
average acceleration = (5.0 m/s - (-3.2 m/s)) / 2.5 s
Simplifying the expression inside the parenthesis, we get:
average acceleration = (5.0 m/s + 3.2 m/s) / 2.5 s
Adding the velocities, we get:
average acceleration = 8.2 m/s / 2.5 s
Dividing the distance by the time, we get:
average acceleration = 3.28 m/s²
Therefore, the car's average acceleration is 3.28 m/s².