A car (m=1606 kg) is travelling down the road at a speed of 10.3 m/s.  The car applies its brakes, which exert a constant force and slows to 6 m/s in a distance of 37.9 metres.  What is the magnitude of the braking force?  Express your answer in Newtons.

To find the magnitude of the braking force applied to the car, we can use the work-energy principle. According to this principle, the work done by the braking force is equal to the change in kinetic energy of the car.

### Step 1: Calculate the initial and final kinetic energies.

The formula for kinetic energy \( KE \) is:

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

where:
- \( m \) is the mass of the car (1606 kg),
- \( v \) is the velocity of the car.

#### Initial kinetic energy:

\[
KE_{\text{initial}} = \frac{1}{2} \times 1606 \times (10.3)^2
\]

#### Final kinetic energy:

\[
KE_{\text{final}} = \frac{1}{2} \times 1606 \times (6)^2
\]

### Step 2: Calculate the change in kinetic energy.

The change in kinetic energy (\( \Delta KE \)) is:

\[
\Delta KE = KE_{\text{final}} - KE_{\text{initial}}
\]

### Step 3: Relate the work done by the braking force to the change in kinetic energy.

Work done by the braking force is given by:

\[
W = F \cdot d
\]

where:
- \( F \) is the magnitude of the braking force,
- \( d \) is the distance over which the braking force acts (37.9 m).

Since the work done by the braking force is equal to the change in kinetic energy (but negative, as the force is decelerating the car):

\[
F \cdot d = -\Delta KE
\]

Thus, the braking force can be calculated as:

\[
F = \frac{-\Delta KE}{d}
\]

Now, I'll compute the values and find the braking force.

Let's calculate.The magnitude of the braking force is approximately \( 1485 \, \text{N} \) (Newtons).

Would you like further details or have any questions?

Here are 5 related questions you could explore:
1. How does the mass of the car affect the magnitude of the braking force?
2. What would the braking force be if the car slowed down to a different speed?
3. How can we calculate the time it took for the car to slow down?
4. How does friction influence the braking force in real-world conditions?
5. What role does acceleration play in determining the braking force?

**Tip:** Always check units in calculations to ensure consistency, especially when working with forces, energy, and distance.

A car (m=1606 kg) is travelling down the road at a speed of 10.3 m/s. The car applies its brakes, which exert a constant force and slows to 6 m/s in a distance of 37.9 metres. What is the magnitude of the braking force? Express your answer in Newtons.

Learn how to calculate the braking force of a car traveling at 10.3 m/s and decelerating to 6 m/s over a distance of 37.9 meters using the work-energy principle. This problem involves concepts of kinematics, kinetic energy, and Newton's laws. Suitable for advanced high school physics students.

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