Stopping distance of a moving vehicle is directly proportional to

Options

A. square of the initial velocity
B. square of the initial acceleration
C. the initial velocity
D. the initial acceleration

Explanation

To determine the stopping distance of a moving vehicle, we need to analyze the factors that contribute to it. The stopping distance is the distance a vehicle travels from the point where the driver perceives a need to stop until the vehicle comes to a complete stop. This distance is influenced by several factors, primarily the vehicle's speed and the deceleration.

### Step-by-Step Solution:

1. **Understanding Stopping Distance**:
The stopping distance (d) can be defined as the distance traveled during the time it takes for the vehicle to come to a stop after the brakes are applied.

2. **Factors Affecting Stopping Distance**:
The stopping distance is affected by:
- Initial speed (v)
- Deceleration (a)
- Reaction time of the driver

3. **Using the Equation of Motion**:
The stopping distance can be derived from the equations of motion. The first equation of motion is:
\[ v^2 = u^2 + 2a s \]
where:
- \(v\) = final velocity (0 m/s when the vehicle stops)
- \(u\) = initial velocity
- \(a\) = acceleration (which will be negative in case of deceleration)
- \(s\) = stopping distance

4. **Rearranging the Equation**:
Since the final velocity \(v\) is 0 when the vehicle stops, we can rearrange the equation:
\[ 0 = u^2 + 2(-a)s \]
This simplifies to:
\[ s = \frac{u^2}{2a} \]

5. **Proportionality**:
From the equation \(s = \frac{u^2}{2a}\), we can see that the stopping distance \(s\) is directly proportional to the square of the initial speed \(u\) (i.e., \(s \propto u^2\)) and inversely proportional to the deceleration \(a\) (i.e., \(s \propto \frac{1}{a}\)).

6. **Conclusion**:
Therefore, the stopping distance of a moving vehicle is directly proportional to the square of the initial speed and inversely proportional to the deceleration.

### Final Answer:
The stopping distance of a moving vehicle is directly proportional to the square of its initial speed.