a driver of a 10 tonne truck travelling at 50 km/h applies brakes fully.
If the trucks brakes apply a total force of 90 kN, calculate the deceleration of the truck.
Calculate how far the truck travel while braking from 50 km/h to 0 km/h

To solve this problem, we need to calculate two things:

1. **The deceleration of the truck**.
2. **The distance the truck travels while braking**.

### 1. Deceleration of the Truck
We start with Newton's second law of motion, which states:
\[
F = ma
\]
Where:
- \( F \) is the force applied (90 kN or 90,000 N),
- \( m \) is the mass of the truck,
- \( a \) is the acceleration (or deceleration, in this case).

First, we convert the mass of the truck from tonnes to kilograms:
\[
m = 10 \, \text{tonnes} = 10 \times 1000 \, \text{kg} = 10,000 \, \text{kg}
\]

Now, using Newton's second law:
\[
a = \frac{F}{m} = \frac{90,000 \, \text{N}}{10,000 \, \text{kg}} = 9 \, \text{m/s}^2
\]

Since the truck is decelerating, the deceleration \( a \) is:
\[
a = -9 \, \text{m/s}^2
\]

### 2. Distance Traveled While Braking
Next, we calculate the distance the truck travels while braking from 50 km/h to 0 km/h.

First, we convert the initial speed from km/h to m/s:
\[
u = 50 \, \text{km/h} = \frac{50 \times 1000 \, \text{m}}{3600 \, \text{s}} \approx 13.89 \, \text{m/s}
\]

The final speed \( v \) is 0 m/s since the truck stops.

Using the equation of motion:
\[
v^2 = u^2 + 2as
\]
Where:
- \( v = 0 \, \text{m/s} \) (final velocity),
- \( u \approx 13.89 \, \text{m/s} \) (initial velocity),
- \( a = -9 \, \text{m/s}^2 \) (deceleration),
- \( s \) is the distance traveled while braking.

Rearranging to solve for \( s \):
\[
0 = (13.89 \, \text{m/s})^2 + 2(-9 \, \text{m/s}^2) \times s
\]
\[
0 = 192.93 \, \text{m}^2/\text{s}^2 - 18 \, \text{m/s}^2 \times s
\]
\[
18s = 192.93
\]
\[
s \approx \frac{192.93}{18} \approx 10.72 \, \text{m}
\]

### Summary:
1. **Deceleration of the truck**: \( 9 \, \text{m/s}^2 \)
2. **Distance traveled while braking**: \( 10.72 \, \text{m} \)

Would you like more details on any part of this solution or have any further questions?

Here are 5 related questions:
1. How would the stopping distance change if the initial speed were higher?
2. What would happen to the deceleration if the braking force were reduced by half?
3. How would the distance traveled while braking change if the truck were heavier?
4. How does the surface (e.g., wet road) affect the stopping distance?
5. What is the relationship between kinetic energy and stopping distance?

**Tip:** Always ensure to convert all units to the SI system before solving physics problems.

Learn how to calculate the deceleration of a 10 tonne truck applying brakes with a force of 90 kN, and determine the braking distance from 50 km/h to 0 km/h. This problem involves Newton's laws of motion and kinematics principles.

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