A body of mass 4 kg is moving with momentum of `8 kg m s^(-1)`. A force of 0.2 N acts on it in the direction of motion of the body for 10 s. The increase in kinetic energy is

Options

A. 10 J
B. 8.5 J
C. 4.5 J
D. 4 J

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the initial velocity (u) of the body
The momentum (P) of the body is given by the formula:
\[ P = m \cdot u \]
Where:
- \( P = 8 \, \text{kg m/s} \)
- \( m = 4 \, \text{kg} \)

Rearranging the formula to find the initial velocity (u):
\[ u = \frac{P}{m} = \frac{8 \, \text{kg m/s}}{4 \, \text{kg}} = 2 \, \text{m/s} \]

### Step 2: Calculate the acceleration (a) caused by the force
The force (F) acting on the body is given as:
\[ F = 0.2 \, \text{N} \]

Using Newton's second law:
\[ a = \frac{F}{m} = \frac{0.2 \, \text{N}}{4 \, \text{kg}} = 0.05 \, \text{m/s}^2 \]

### Step 3: Calculate the final velocity (v) after 10 seconds
Using the formula for final velocity:
\[ v = u + a \cdot t \]
Where:
- \( t = 10 \, \text{s} \)

Substituting the values:
\[ v = 2 \, \text{m/s} + (0.05 \, \text{m/s}^2 \cdot 10 \, \text{s}) \]
\[ v = 2 \, \text{m/s} + 0.5 \, \text{m/s} = 2.5 \, \text{m/s} \]

### Step 4: Calculate the initial kinetic energy (KE_initial)
The initial kinetic energy (KE_initial) can be calculated using the formula:
\[ KE = \frac{1}{2} m u^2 \]

Substituting the values:
\[ KE_{\text{initial}} = \frac{1}{2} \cdot 4 \, \text{kg} \cdot (2 \, \text{m/s})^2 \]
\[ KE_{\text{initial}} = \frac{1}{2} \cdot 4 \cdot 4 = 8 \, \text{J} \]

### Step 5: Calculate the final kinetic energy (KE_final)
The final kinetic energy (KE_final) can be calculated using the formula:
\[ KE = \frac{1}{2} m v^2 \]

Substituting the values:
\[ KE_{\text{final}} = \frac{1}{2} \cdot 4 \, \text{kg} \cdot (2.5 \, \text{m/s})^2 \]
\[ KE_{\text{final}} = \frac{1}{2} \cdot 4 \cdot 6.25 = 12.5 \, \text{J} \]

### Step 6: Calculate the increase in kinetic energy
The increase in kinetic energy (ΔKE) is given by:
\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
\[ \Delta KE = 12.5 \, \text{J} - 8 \, \text{J} = 4.5 \, \text{J} \]

### Final Answer
The increase in kinetic energy is \( 4.5 \, \text{J} \).

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