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The problem is asking for the amount of work required to accelerate a car from rest to a certain speed. 

To find the work required to accelerate the car, we use the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.

The kinetic energy \( KE \) of an object is given by:

\[
KE = \frac{1}{2} m v^2
\]

Where:
- \( m \) is the mass of the car (in kg),
- \( v \) is the final velocity (in m/s).

### Given:
- Mass of the car \( m = 1800 \, \text{kg} \),
- Final velocity \( v = 12.0 \, \text{m/s} \),
- Initial velocity \( u = 0 \, \text{m/s} \) (since the car starts from rest).

The change in kinetic energy is:

\[
\Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2
\]

Since \( u = 0 \):

\[
\Delta KE = \frac{1}{2} m v^2
\]

Now, let's calculate the work required:

\[
W = \frac{1}{2} \times 1800 \, \text{kg} \times (12.0 \, \text{m/s})^2
\]

I'll calculate the result.The work required to accelerate the 1800 kg car from rest to a speed of 12.0 m/s is 129,600 joules (J).

Would you like more details on this calculation or have any questions? Here are some related questions:

1. How does the mass of the car affect the work required to accelerate it?
2. What if the car was already moving at 5 m/s; how would you calculate the work required to increase its speed to 12 m/s?
3. How does increasing the final speed impact the work required?
4. How would air resistance or friction impact the total work required in real-world scenarios?
5. How is power related to work, and how can you calculate the power if the acceleration happens in 10 seconds?

**Tip:** Always remember that work depends on the change in kinetic energy, not just the final speed or mass alone.

How much work is required to accelerate a 1800 kg car from rest to a speed of 12.0 m/s?

Learn how to calculate the work required to accelerate an 1800 kg car from rest to a speed of 12 m/s. This problem uses the Work-Energy Theorem and Kinetic Energy formulas, suitable for students in Grades 9-12.

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