When the speed of a car is `u`, the mimimum distance over which it canbe stopped is `a`, If speed becomes `nu`, what will be the mimimum distance over which it can be stopped during the same time?

Options

A. ` s//h`
B. ` ns`
C. ` s//n^(2)`
D. `n^(2) s`

Explanation

To solve the problem, we need to analyze the stopping distance of a car when its speed changes.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- When the speed of the car is \( u \), the minimum stopping distance is \( a \).
- We need to find the stopping distance when the speed becomes \( nu \) (where \( n \) is a constant multiplier).

2. **Using the Formula for Stopping Distance**:
- The stopping distance \( S \) can be calculated using the formula:
\[ S = \frac{u^2}{2a} \]
- Here, \( u \) is the initial speed, and \( a \) is the deceleration (retardation).

3. **Finding the Stopping Distance for Speed \( nu \)**:
- When the speed is \( nu \), the stopping distance \( S' \) can be expressed as:
\[ S' = \frac{(nu)^2}{2a'} \]
- Here, \( a' \) is the deceleration when the speed is \( nu \).

4. **Relating the Deceleration**:
- Since the time taken to stop is the same in both cases, we can relate the decelerations.
- The time \( t \) to stop from speed \( u \) is:
\[ t = \frac{u}{a} \]
- The time \( t \) to stop from speed \( nu \) is:
\[ t = \frac{nu}{a'} \]
- Setting these equal gives:
\[ \frac{u}{a} = \frac{nu}{a'} \]
- Rearranging this gives:
\[ a' = \frac{a}{n} \]

5. **Substituting Back into the Stopping Distance Formula**:
- Now substitute \( a' \) back into the stopping distance formula for \( nu \):
\[ S' = \frac{(nu)^2}{2 \cdot \frac{a}{n}} = \frac{n^2 u^2}{\frac{2a}{n}} = \frac{n^3 u^2}{2a} \]

6. **Relating to the Original Stopping Distance**:
- From the original stopping distance \( a = \frac{u^2}{2a} \), we can express \( \frac{u^2}{2a} \) as \( a \).
- Thus, we can rewrite \( S' \) in terms of \( a \):
\[ S' = n^2 a \]

### Final Result:
The minimum distance over which the car can be stopped when its speed becomes \( nu \) is:
\[ S' = n^2 a \]