a car rolling down an incline for 5.0 seconds has an acceleration of 4.0m/s$$ ^2 $$. If the cart has a beginnings speed of 2.0m/s, what is it's final speed?

To find the final speed ($ v_f $) of the car after 5.0 seconds, we can use the following kinematic equation:

\[
v_f = v_i + at
\]

Where:
- $ v_f $ is the final velocity (what we are solving for),
- $ v_i = 2.0 \, \text{m/s} $ is the initial velocity,
- $ a = 4.0 \, \text{m/s}^2 $ is the acceleration,
- $ t = 5.0 \, \text{seconds} $ is the time.

Now substitute the given values into the equation:

\[
v_f = 2.0 \, \text{m/s} + (4.0 \, \text{m/s}^2)(5.0 \, \text{seconds})
\]

\[
v_f = 2.0 \, \text{m/s} + 20.0 \, \text{m/s}
\]

\[
v_f = 22.0 \, \text{m/s}
\]

So, the car's final speed is **22.0 m/s**.

Would you like more details or have any questions?

Here are some related questions to explore:
1. What would happen if the car had no initial speed?
2. How far did the car travel in the 5.0 seconds?
3. How would the final speed change if the incline caused a lower acceleration?
4. What would the final velocity be after 10 seconds with the same conditions?
5. How does the direction of acceleration affect the motion?

**Tip**: Always pay attention to units when calculating acceleration and velocity!

A car rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s². If the cart has a beginning speed of 2.0 m/s, what is its final speed?

Discover how to calculate the final speed of a car rolling down an incline with an acceleration of 4.0 m/s² over 5.0 seconds, starting with an initial speed of 2.0 m/s. This kinematics problem introduces students to key concepts in linear motion and acceleration, ideal for Grades 9-12.

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