a car is initially moving at 20m/s. the car then accelerates at a rate of 5m/s^2. how fast will the car be moving after 400 meters

To solve this problem, we can use the following kinematic equation:

\[
v^2 = u^2 + 2as
\]

Where:
- \( v \) is the final velocity (what we are trying to find),
- \( u \) is the initial velocity (\( u = 20 \, \text{m/s} \)),
- \( a \) is the acceleration (\( a = 5 \, \text{m/s}^2 \)),
- \( s \) is the displacement (\( s = 400 \, \text{m} \)).

Let's plug in the values and solve for \( v \):

\[
v^2 = (20)^2 + 2(5)(400)
\]
\[
v^2 = 400 + 4000
\]
\[
v^2 = 4400
\]
\[
v = \sqrt{4400} \approx 66.33 \, \text{m/s}
\]

So, the car will be moving at approximately **66.33 m/s** after traveling 400 meters.

Would you like more details on any step, or do you have any other questions?

Here are some related questions you might explore:
1. How long will it take for the car to travel the 400 meters?
2. What would the velocity be if the acceleration was 3 m/s² instead?
3. How far will the car travel in 10 seconds under this acceleration?
4. If the car decelerates at 5 m/s², how long will it take to stop?
5. What is the car’s average velocity over the 400-meter distance?

**Tip:** When solving kinematic problems, always ensure you correctly identify the known variables and choose the appropriate equation accordingly.

A car is initially moving at 20m/s. The car then accelerates at a rate of 5m/s^2. How fast will the car be moving after 400 meters?

Learn how to calculate the final velocity of a car initially moving at 20m/s with an acceleration of 5m/s² after traveling 400 meters. This problem uses the kinematic equation v² = u² + 2as and is suitable for students in Grades 9-12.

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