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).