A car has a rear view mirror of radius of curvature 2 m. A motorcycle is approaching the car at `15 m//s`. If the car is stationary, how fast is the image of the bike approaching the car when the bike is 40 m away?

Explanation

To solve the problem, we need to find how fast the image of the motorcycle is approaching the car when the motorcycle is 40 m away. We will use the mirror formula and the concept of relative velocities.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Radius of curvature of the mirror, \( R = 2 \, \text{m} \)
- Velocity of the motorcycle, \( \frac{du}{dt} = -15 \, \text{m/s} \) (negative because it is approaching the car)
- Distance of the motorcycle from the mirror, \( u = -40 \, \text{m} \) (negative as per sign convention)
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