If a car slows from 22 m/s with an acceleration of -2.0 m/s^2. How long does it require to get 4 m/s?

To determine the time required for the car to slow down from 22 m/s to 4 m/s with a given acceleration, we can use the following kinematic equation:

\[
v_f = v_i + a \cdot t
\]

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

Given:
- Initial velocity, \( v_i = 22 \, \text{m/s} \)
- Final velocity, \( v_f = 4 \, \text{m/s} \)
- Acceleration, \( a = -2.0 \, \text{m/s}^2 \) (negative because it is a deceleration)

We want to find the time \( t \).

Rearranging the equation to solve for \( t \):

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

Plugging in the values:

\[
t = \frac{4 \, \text{m/s} - 22 \, \text{m/s}}{-2.0 \, \text{m/s}^2}
\]

\[
t = \frac{-18 \, \text{m/s}}{-2.0 \, \text{m/s}^2}
\]

\[
t = 9 \, \text{s}
\]

Therefore, it takes **9 seconds** for the car to slow down from 22 m/s to 4 m/s with an acceleration of \(-2.0 \, \text{m/s}^2\).

Would you like to see more details or have any other questions?

Here are 5 related questions to consider:

1. What distance does the car cover during this deceleration?
2. What would be the time required if the acceleration was \(-3.0 \, \text{m/s}^2\)?
3. If the car starts at a different initial velocity, how would that affect the time to reach 4 m/s?
4. How long would it take for the car to come to a complete stop from 22 m/s with the same acceleration?
5. What happens if the acceleration is positive instead of negative?

**Tip:** When working with deceleration, ensure to use the correct sign for acceleration (negative) to reflect the slowing down in calculations.

Learn how to calculate the time required for a car to decelerate from 22 m/s to 4 m/s using kinematic equations. Understand the impact of acceleration on velocity changes in physics problems. Suitable for high school students studying physics.

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