A car of 18,000 N that starts from rest acquires a speed of 100 km/h in a distance of 208.42 meters. Find the magnitude of the applied force.

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

### Step 1: Convert the speed to meters per second
The speed is given as 100 km/h. We convert this to meters per second:

\[
100 \, \text{km/h} = 100 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 27.78 \, \text{m/s}
\]

### Step 2: Calculate the car's kinetic energy
The kinetic energy (\(K\)) of the car when it reaches 27.78 m/s is given by:

\[
K = \frac{1}{2}mv^2
\]

First, find the mass \(m\) using the car's weight. The weight \(W\) is related to mass by:

\[
W = mg \quad \Rightarrow \quad m = \frac{W}{g}
\]

Given \(W = 18000 \, \text{N}\) and \(g = 9.81 \, \text{m/s}^2\):

\[
m = \frac{18000 \, \text{N}}{9.81 \, \text{m/s}^2} = 1834.37 \, \text{kg}
\]

Now, calculate the kinetic energy:

\[
K = \frac{1}{2} \times 1834.37 \, \text{kg} \times (27.78 \, \text{m/s})^2 = 707000.8 \, \text{J}
\]

### Step 3: Apply the work-energy principle
The work done by the applied force (\(F\)) over the distance \(d = 208.42 \, \text{m}\) is equal to the kinetic energy:

\[
W = F \times d = K
\]

Solve for \(F\):

\[
F = \frac{K}{d} = \frac{707000.8 \, \text{J}}{208.42 \, \text{m}} = 3392.2 \, \text{N}
\]

### Answer:
The magnitude of the applied force is approximately **3392.2 N**.

Would you like to go over any particular detail? Here are some related questions that might interest you:

1. What is the work-energy principle?
2. How do you convert between different units of speed?
3. What are the factors affecting the kinetic energy of an object?
4. How does mass affect the force required to accelerate an object?
5. What role does friction play in the motion of a vehicle?

**Tip:** Always make sure to use consistent units when solving physics problems to avoid errors in calculation.

Learn how to calculate the magnitude of the applied force using the work-energy principle with a detailed step-by-step solution. This physics problem involves determining the force required to accelerate a car from rest to a speed of 100 km/h over a distance of 208.42 meters. Suitable for high school students studying physics.

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