A car is moving with a velocity V. The car driver sees a truck at rest at a distance s. To avoid collision which is better, to apply brake or to turn sharply ?

Explanation

To determine whether the car driver should apply the brakes or turn sharply to avoid a collision with the truck, we can analyze the situation using the principles of circular motion and friction.

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- The car is moving with an initial velocity \( V \).
- The truck is at rest at a distance \( s \) from the car.

2. **Applying Brakes**:
- When the driver applies the brakes, the car experiences a deceleration due to friction.
- The deceleration \( a \) can be expressed as:
\[ a = -\frac{F_r}{m} \]
where \( F_r \) is the frictional force and \( m \) is the mass of the car.

3. **Using the Kinematic Equation**:
- We can use the kinematic equation:
\[ V_f^2 = V_i^2 + 2a d \]
In this case, the final velocity \( V_f \) will be 0 (the car comes to a stop), the initial velocity \( V_i = V \), and the distance \( d = s \).
- Substituting these values, we get:
\[ 0 = V^2 + 2(-\frac{F_r}{m})s \]
- Rearranging gives:
\[ \frac{F_r}{m} = \frac{V^2}{2s} \]

4. **Turning Sharply**:
- If the driver decides to turn sharply, the frictional force must provide the necessary centripetal force to keep the car moving in a circular path.
- The centripetal force required is given by:
\[ F_c = \frac{mV^2}{r} \]
where \( r \) is the radius of the turn. In this case, we can assume \( r \) is approximately equal to \( s \) for a sharp turn.
- Therefore, the frictional force in this case must satisfy:
\[ F_r = \frac{mV^2}{s} \]

5. **Comparison of Frictional Forces**:
- From the two scenarios, we have:
- For braking: \( F_r = \frac{mV^2}{2s} \)
- For turning sharply: \( F_r = \frac{mV^2}{s} \)
- Comparing these two, we see that the frictional force required for turning sharply is greater than that required for braking:
\[ \frac{mV^2}{2s} < \frac{mV^2}{s} \]
- This indicates that the friction available when braking is less than that required for a sharp turn.

6. **Conclusion**:
- Since the friction required to turn sharply is greater than the friction available when braking, it is safer for the driver to apply the brakes rather than to turn sharply to avoid a collision.

### Final Answer:
The driver should apply the brakes to avoid a collision with the truck.

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