The driver of a car travelling at velocity v suddenly see a broad wall in front of him at a distance d. He should

Options

A. break sharply
B. turn sharply
C. both (a) and (b)
D. none of these

Answer

To solve the problem of how a driver should react when he suddenly sees a wall in front of him while traveling at a velocity \( v \) and at a distance \( d \), we can analyze the situation using the principles of physics, specifically the concepts of motion, forces, and energy.

### Step-by-Step Solution:

1. **Identify the Situation**:
The driver is traveling at a speed \( v \) and sees a wall at a distance \( d \). The driver must decide whether to brake sharply, turn sharply, or do neither.

2. **Understand the Forces Involved**:
When the driver applies the brakes, the car experiences a retarding force \( F \). This force is typically due to friction between the tires and the road.

3. **Calculate the Stopping Distance**:
The kinetic energy of the car when traveling at speed \( v \) is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the car. When the brakes are applied, this kinetic energy is converted into work done against the retarding force \( F \):
\[ \frac{1}{2} mv^2 = F \cdot x \]
where \( x \) is the stopping distance. Rearranging this gives:
\[ x = \frac{mv^2}{2F} \]

4. **Determine the Required Stopping Distance**:
The driver needs to stop the car before reaching the wall. Therefore, the stopping distance \( x \) must be less than or equal to the distance \( d \):
\[ x \leq d \]
This means:
\[ \frac{mv^2}{2F} \leq d \]

5. **Consider the Turning Option**:
If the driver decides to turn instead of braking, the centripetal force required to make the turn is given by:
\[ F_c = \frac{mv^2}{r} \]
where \( r \) is the radius of the turn. For the car to turn safely, the available friction must provide enough force to allow the turn without skidding.

6. **Compare the Two Options**:
- If the stopping distance \( x \) is greater than \( d \), then the driver cannot stop in time and must turn.
- If the stopping distance \( x \) is less than or equal to \( d \), the driver should brake sharply.

7. **Conclusion**:
The safest and most effective action for the driver is to brake sharply if the stopping distance is less than or equal to the distance to the wall. Otherwise, the driver should attempt to turn.

### Final Answer:
The driver should **brake sharply**.