A 25,000 N bus is traveling at a speed of 80 km/h and comes to a complete stop in 10 seconds. What was your braking force?

To find the braking force, we can apply the concept of Newton's second law of motion, \( F = ma \). Here, we need to calculate the deceleration of the bus and then use that to determine the force.

### Given Data:
- Weight of the bus: \( W = 25,000 \, \text{N} \)
- Initial speed of the bus: \( v_i = 80 \, \text{km/h} \)
- Final speed of the bus: \( v_f = 0 \, \text{m/s} \)
- Time taken to stop: \( t = 10 \, \text{seconds} \)

### Steps:
1. **Convert the initial speed from km/h to m/s**:
   \[
   v_i = 80 \, \text{km/h} = \left( \frac{80 \times 1000}{3600} \right) \, \text{m/s} = 22.22 \, \text{m/s}
   \]

2. **Calculate the acceleration (deceleration)**:
   The acceleration (a) can be calculated using the formula:
   \[
   a = \frac{v_f - v_i}{t} = \frac{0 - 22.22}{10} = -2.22 \, \text{m/s}^2
   \]
   (Note that the negative sign indicates deceleration.)

3. **Find the mass of the bus**:
   Weight \( W = mg \), so:
   \[
   m = \frac{W}{g} = \frac{25,000 \, \text{N}}{9.8 \, \text{m/s}^2} = 2,551.02 \, \text{kg}
   \]

4. **Calculate the braking force**:
   Using \( F = ma \):
   \[
   F = 2,551.02 \, \text{kg} \times (-2.22 \, \text{m/s}^2) = -5,666.26 \, \text{N}
   \]

The magnitude of the braking force is approximately \( 5,666.26 \, \text{N} \).

Would you like more details on any of the steps, or do you have any questions?

Here are some related questions:
1. How does weight affect braking force?
2. What happens if the deceleration time is increased?
3. How do factors like road condition influence braking distance?
4. What is the relation between braking force and stopping distance?
5. How does the mass of the vehicle impact its stopping force?

**Tip:** Always ensure the units are consistent when performing calculations in physics.

Learn how to calculate the braking force of a bus using Newton's second law of motion. This physics problem involves determining the braking force based on the bus's weight, initial speed, final speed, and stopping time. Suitable for high school students studying physics.

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