The driver of a car travelling at velocity v suddenly sees a braood with in front of him at a distance a, He should

Options

A. brake sharply
B. turn sharply
C. (a) & (b) both
D. none of the above

Answer

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

### Step-by-Step Solution:

1. **Understanding the Situation**: The driver is traveling towards a wall at a speed \( v \) and sees the wall at a distance \( a \). The driver has two options: to brake sharply or to turn sharply.

2. **Applying the Work-Energy Theorem**: When the driver applies the brakes, the kinetic energy of the car is converted into work done against friction. According to the work-energy theorem:
\[ \frac{1}{2} mv^2 = \text{Work done} = f \cdot x \]
where \( m \) is the mass of the car, \( v \) is the initial velocity, \( f \) is the friction force, and \( x \) is the stopping distance.

3. **Deriving the Stopping Distance**: Rearranging the equation gives us:
\[ x = \frac{1}{2} \frac{mv^2}{f} \]
This equation shows that the stopping distance \( x \) depends on the initial velocity \( v \) and the friction force \( f \).

4. **Considering the Turning Option**: If the driver decides to turn, the centripetal force required to keep the car moving in a circular path is given by:
\[ f = \frac{mv^2}{r} \]
where \( r \) is the radius of the turn. Rearranging this gives:
\[ r = \frac{mv^2}{f} \]

5. **Comparing Stopping and Turning Distances**: From the two equations derived, we can compare the stopping distance \( x \) and the turning radius \( r \). If we set:
\[ x = \frac{r}{2} \]
This implies that the stopping distance is less than the distance required to make a turn.

6. **Conclusion**: Since the stopping distance \( x \) is less than the distance \( a \) (the distance to the wall), the driver should brake sharply to avoid crashing into the wall. Therefore, the correct option is to brake sharply.

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