A car accelerates from 10 m/s to 30 m/s. If the acceleration is 22m/s 2 , how far does
the car travel?

We can solve this using one of the kinematic equations of motion. The equation that relates initial velocity (\(v_0\)), final velocity (\(v\)), acceleration (\(a\)), and displacement (\(d\)) is:

\[
v^2 = v_0^2 + 2ad
\]

Where:
- \(v_0 = 10 \, \text{m/s}\) (initial velocity),
- \(v = 30 \, \text{m/s}\) (final velocity),
- \(a = 22 \, \text{m/s}^2\) (acceleration),
- \(d\) is the distance traveled (which we are trying to find).

### Step 1: Rearrange the formula to solve for distance \(d\):
\[
d = \frac{v^2 - v_0^2}{2a}
\]

### Step 2: Plug in the known values:
\[
d = \frac{(30)^2 - (10)^2}{2 \times 22}
\]

Now let's compute that:

\[
d = \frac{900 - 100}{44} = \frac{800}{44} \approx 18.18 \, \text{meters}
\]

### Final answer:
The car travels approximately **18.18 meters**.

Do you need any further details or explanations?

Here are 5 related questions to consider:
1. How would the distance change if the acceleration was halved?
2. What time does the car take to reach its final velocity?
3. What is the average velocity of the car during this acceleration?
4. How much distance would the car cover if the initial velocity were zero?
5. What would happen to the distance if the final velocity were doubled?

**Tip:** Always keep the units consistent when solving physics problems to avoid errors in calculation!

A car accelerates from 10 m/s to 30 m/s. If the acceleration is 22 m/s², how far does the car travel?

Discover how to calculate the distance traveled by a car accelerating from 10 m/s to 30 m/s with an acceleration of 22 m/s². Using kinematic equations, this problem explores motion concepts for students in Grades 9-12.

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