A car moving with a speed of `40 km//h` can be stopped by applying the brakes after at least 2 m. If the same car is moving with a speed of `80 km//h`, what is the minimum stopping distance?

Options

A. 8 m
B. 2 m
C. 4 m
D. 6 m

Explanation

To solve the problem of determining the minimum stopping distance of a car moving at 80 km/h, we can use the relationship between stopping distance and speed. Here's a step-by-step solution:

### Step 1: Understand the relationship between speed and stopping distance
The stopping distance (s) is directly proportional to the square of the speed (u). This can be expressed mathematically as:
\[ s \propto u^2 \]
This means that if we know the stopping distance at one speed, we can find it at another speed by using the ratio of the squares of the speeds.

### Step 2: Define the known values
From the problem, we have:
- Speed \( u_1 = 40 \, \text{km/h} \)
- Stopping distance \( s_1 = 2 \, \text{m} \)
- Speed \( u_2 = 80 \, \text{km/h} \)

### Step 3: Set up the proportion
Using the proportionality established in Step 1, we can write:
\[ \frac{s_1}{s_2} = \frac{u_1^2}{u_2^2} \]
Where \( s_2 \) is the stopping distance we need to find.

### Step 4: Substitute the known values into the equation
Substituting the known values into the proportion gives us:
\[ \frac{2}{s_2} = \frac{(40)^2}{(80)^2} \]

### Step 5: Calculate the squares of the speeds
Calculating the squares:
- \( (40)^2 = 1600 \)
- \( (80)^2 = 6400 \)

So we have:
\[ \frac{2}{s_2} = \frac{1600}{6400} \]

### Step 6: Simplify the fraction
The fraction \( \frac{1600}{6400} \) simplifies to:
\[ \frac{1}{4} \]
Thus, we can rewrite the equation as:
\[ \frac{2}{s_2} = \frac{1}{4} \]

### Step 7: Cross-multiply to solve for \( s_2 \)
Cross-multiplying gives:
\[ 2 \cdot 4 = s_2 \implies s_2 = 8 \, \text{m} \]

### Conclusion
The minimum stopping distance when the car is moving at 80 km/h is:
\[ \boxed{8 \, \text{m}} \]