A body of mass 40kg resting on a rough horizontal surface is subjected to a force `P` which is just enough to start the motion of the body. If `mu_(s)=0.5mu_(k)=0.4 , g=10ms^(-2)` an dthe force `P` is continuously applied on the body, then the accceleration of the body is.

Options

A. zero
B. `1 ms^(-2)`
C. `2 ms^(-2)`
D. `2.4 ms^(-2)`

Explanation

To solve the problem step by step, we will analyze the forces acting on the body and apply Newton's laws of motion.

### Step 1: Identify the forces acting on the body
- The body has a mass \( m = 40 \, \text{kg} \).
- The gravitational force acting downwards is \( F_g = mg = 40 \, \text{kg} \times 10 \, \text{m/s}^2 = 400 \, \text{N} \).
- The normal force \( N \) acting upwards is equal to the gravitational force when the body is at rest: \( N = F_g = 400 \, \text{N} \).

### Step 2: Calculate the static friction force
- The maximum static friction force \( F_s \) that can act on the body before it starts moving is given by:
\[ F_s = \mu_s \cdot N \]
- Given \( \mu_s = 0.5 \):
\[ F_s = 0.5 \cdot 400 \, \text{N} = 200 \, \text{N} \]

### Step 3: Determine the force \( P \) required to start the motion
- The force \( P \) that just starts the motion is equal to the maximum static friction force:
\[ P = F_s = 200 \, \text{N} \]

### Step 4: Analyze the motion after the body starts moving
- Once the body starts moving, the kinetic friction force \( F_k \) will act against the motion. The kinetic friction force is given by:
\[ F_k = \mu_k \cdot N \]
- Given \( \mu_k = 0.4 \):
\[ F_k = 0.4 \cdot 400 \, \text{N} = 160 \, \text{N} \]

### Step 5: Apply Newton's second law to find the acceleration
- The net force \( F_{net} \) acting on the body when it is in motion is:
\[ F_{net} = P - F_k \]
- Substituting the values:
\[ F_{net} = 200 \, \text{N} - 160 \, \text{N} = 40 \, \text{N} \]
- According to Newton's second law, \( F_{net} = m \cdot a \):
\[ 40 \, \text{N} = 40 \, \text{kg} \cdot a \]
- Solving for \( a \):
\[ a = \frac{40 \, \text{N}}{40 \, \text{kg}} = 1 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the body is \( 1 \, \text{m/s}^2 \).

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