Consider a car moving on a straight road with a speed of `100m//s`. The distance at which car can be stopped is `[mu_k=0.5]`

Options

A. (a)400 m
B. (b)100 m
C. (c)1000m
D. (d)800m

Explanation

To solve the problem of determining the stopping distance of a car moving at a speed of 100 m/s with a coefficient of kinetic friction (μ_k) of 0.5, we can use the equations of motion and the relationship between frictional force and acceleration.

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial velocity (u) = 100 m/s
- Final velocity (v) = 0 m/s (since the car stops)
- Coefficient of kinetic friction (μ_k) = 0.5
- Acceleration due to gravity (g) = 9.81 m/s² (approximately 10 m/s² for simplicity)

2. **Determine the acceleration (a):**
The acceleration due to friction can be calculated using the formula:
\[ a = -\mu_k \cdot g \]
Substituting the values:
\[ a = -0.5 \cdot 10 = -5 \text{ m/s}^2 \]

3. **Use the equation of motion:**
We can apply the equation of motion:
\[ v^2 = u^2 + 2as \]
Rearranging for stopping distance (s):
\[ s = \frac{v^2 - u^2}{2a} \]
Substituting the known values:
\[ s = \frac{0^2 - (100)^2}{2 \cdot (-5)} \]

4. **Calculate the stopping distance (s):**
\[ s = \frac{-10000}{-10} = 1000 \text{ m} \]

5. **Conclusion:**
The distance at which the car can be stopped is **1000 meters**.