Calculate the force (in N) needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). Assume positive forces in the direction of motion.

To find the force required to bring the car to rest, we can use the following approach.

### Step 1: Convert Speed to Meters per Second
The car's initial speed is given in km/h, so we need to convert it to m/s.

\[
90.0 \, \text{km/h} = 90.0 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 25.0 \, \text{m/s}
\]

### Step 2: Use Kinematic Equation to Find Acceleration
We know:
- Initial velocity (\( v_0 \)) = 25.0 m/s
- Final velocity (\( v \)) = 0 m/s (since the car is coming to rest)
- Distance (\( d \)) = 120 m

Using the kinematic equation:

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

Rearrange to solve for acceleration (\( a \)):

\[
a = \frac{v^2 - v_0^2}{2d} = \frac{0^2 - (25.0)^2}{2 \times 120} = \frac{-625}{240} = -2.604 \, \text{m/s}^2
\]

The acceleration is negative, indicating deceleration.

### Step 3: Apply Newton’s Second Law to Find Force
Using Newton’s second law:

\[
F = ma
\]

where:
- \( m = 950 \, \text{kg} \)
- \( a = -2.604 \, \text{m/s}^2 \)

So:

\[
F = 950 \times (-2.604) = -2473.8 \, \text{N}
\]

### Final Answer
Since we want the magnitude of the force (direction is given by context), the required force is:

\[
\text{Force} = 2473.8 \, \text{N}
\]

Let me know if you want further details or have any questions.

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Here are some related questions to extend your understanding:
1. How would the force change if the stopping distance were increased to 200 m?
2. What would be the required force if the car's mass were doubled?
3. How would adding a slope affect the force needed to stop the car?
4. What if the initial speed were 120 km/h instead of 90 km/h?
5. How does friction affect real-life stopping distances?

**Tip:** Remember that converting units correctly is essential for accurate calculations, especially when switching between speed (m/s) and force (N).

Learn how to calculate the force required to bring a 950-kg car to rest from 90 km/h over a distance of 120 meters. This physics problem explores kinematic equations, unit conversion, and Newton's Second Law, making it suitable for high school students.

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