On a level road, a scooterist applies brakes to slow down from a speed of 10 m/s to 5 m/s. If the mass of the scooterist and the scooter be 150 kg, calculate the work done by the brakes. (Neglect air resistance and friction)

Explanation

To solve the problem of calculating the work done by the brakes when a scooter slows down from a speed of 10 m/s to 5 m/s, we will use the concept of kinetic energy and the work-energy theorem.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Initial speed (u) = 10 m/s
- Final speed (v) = 5 m/s
- Mass (m) = 150 kg

2. **Calculate Initial Kinetic Energy (KE_initial):**
- The formula for kinetic energy is given by:
\[ KE = \frac{1}{2} m v^2 \]
- Therefore, the initial kinetic energy when the scooter is traveling at 10 m/s is:
\[ KE_{\text{initial}} = \frac{1}{2} \times 150 \, \text{kg} \times (10 \, \text{m/s})^2 \]
\[ KE_{\text{initial}} = \frac{1}{2} \times 150 \times 100 = 7500 \, \text{J} \]

3. **Calculate Final Kinetic Energy (KE_final):**
- Now, we calculate the final kinetic energy when the scooter slows down to 5 m/s:
\[ KE_{\text{final}} = \frac{1}{2} \times 150 \, \text{kg} \times (5 \, \text{m/s})^2 \]
\[ KE_{\text{final}} = \frac{1}{2} \times 150 \times 25 = 1875 \, \text{J} \]

4. **Calculate the Work Done by the Brakes:**
- According to the work-energy theorem, the work done (W) by the brakes is equal to the change in kinetic energy:
\[ W = KE_{\text{final}} - KE_{\text{initial}} \]
\[ W = 1875 \, \text{J} - 7500 \, \text{J} = -5625 \, \text{J} \]

5. **Interpret the Result:**
- The negative sign indicates that the work done by the brakes is in the opposite direction to the motion of the scooter, which is expected as the brakes are slowing it down.

### Final Answer:
The work done by the brakes is **-5625 J**.

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