A race car accelerates from 0 m/s to 30 m/s with a displacement of 60 m. What is the vehicle's acceleration?

We can find the vehicle's acceleration using the **kinematic equation** that relates velocity, displacement, and acceleration:

\[
v^2 = u^2 + 2a s
\]

Where:
- \(v\) is the final velocity (30 m/s),
- \(u\) is the initial velocity (0 m/s),
- \(a\) is the acceleration (what we're solving for),
- \(s\) is the displacement (60 m).

Now, plugging in the known values:

\[
(30)^2 = (0)^2 + 2 \cdot a \cdot 60
\]

This simplifies to:

\[
900 = 120a
\]

Now, solve for \(a\):

\[
a = \frac{900}{120} = 7.5 \, \text{m/s}^2
\]

So, the vehicle's acceleration is **7.5 m/s²**.

Would you like more details or have any questions?

Here are some related questions for further practice:
1. What would the acceleration be if the car reached 40 m/s over the same displacement?
2. How long did the car take to reach 30 m/s with this acceleration?
3. If the car maintained this acceleration, what would its velocity be after covering 100 meters?
4. What is the car's displacement if it reaches 30 m/s in 3 seconds?
5. How much time does it take to cover the 60 meters with this acceleration?

**Tip:** In kinematics, always check the given information carefully to choose the correct equation for the unknown quantity!

Learn how to calculate the acceleration of a race car that accelerates from 0 m/s to 30 m/s with a displacement of 60 meters. This problem uses the kinematic equation v^2 = u^2 + 2as and is ideal for students in Grades 9-12 studying uniform acceleration.

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