The co-efficient of static & kinetic friction are 0.6 & 0.3 The minimum horizontal force required to start the motion is applied and if it is continued, the distance travelled by the body in 4 sec is (g=10 `ms^(-2)`)

Options

A. 6 m
B. 24 m
C. 2.4 m
D. 5 m

Answer

To solve the problem step by step, we will follow the principles of friction and kinematics.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Coefficient of static friction, \( \mu_s = 0.6 \)
- Coefficient of kinetic friction, \( \mu_k = 0.3 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)
- Time, \( t = 4 \, \text{s} \)

2. **Determine the Force of Kinetic Friction:**
- When the body is in motion, the force of kinetic friction \( F_k \) can be calculated using the formula:
\[ F_k = \mu_k \cdot m \cdot g \]
- Substituting the values:
\[ F_k = 0.3 \cdot m \cdot 10 = 3m \]

3. **Calculate the Acceleration of the Body:**
- According to Newton's second law, the net force acting on the body is equal to the mass times the acceleration \( a \):
\[ F_{net} = m \cdot a \]
- The only horizontal force acting on the body is the applied force minus the kinetic friction. Since the applied force is just enough to overcome the kinetic friction, we can set:
\[ F_{applied} = F_k = 3m \]
- Therefore, the acceleration \( a \) can be calculated as:
\[ a = \frac{F_k}{m} = \frac{3m}{m} = 3 \, \text{m/s}^2 \]

4. **Use the Kinematic Equation to Find Distance:**
- The distance \( s \) traveled by the body in time \( t \) can be calculated using the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
- Since the initial velocity \( u = 0 \) (the body starts from rest), the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]
- Substituting the values of \( a \) and \( t \):
\[ s = \frac{1}{2} \cdot 3 \cdot (4^2) = \frac{1}{2} \cdot 3 \cdot 16 = \frac{48}{2} = 24 \, \text{m} \]

5. **Final Result:**
- The distance traveled by the body in 4 seconds is \( 24 \, \text{m} \).

### Summary:
The minimum horizontal force required to start the motion is applied, and the distance traveled by the body in 4 seconds is **24 meters**.