A uniform force of 4 N acts on a body of mass 40 kg for a distance of 2 m. The kinetic energy acquired by the body is

Options

A. 460J
B. 800J
C. 320J
D. 8J

Answer

To find the kinetic energy acquired by a body when a uniform force acts on it, we can follow these steps:

### Step 1: Identify the given values
- Force (F) = 4 N
- Mass (m) = 40 kg
- Distance (s) = 2 m

### Step 2: Calculate the acceleration (a)
Using Newton's second law of motion, we can calculate the acceleration:
\[ F = m \cdot a \]
Rearranging gives:
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{4 \, \text{N}}{40 \, \text{kg}} = 0.1 \, \text{m/s}^2 \]

### Step 3: Use the kinematic equation to find final velocity (v)
We can use the following kinematic equation, where initial velocity (u) is 0 (the body starts from rest):
\[ v^2 = u^2 + 2as \]
Substituting the known values:
\[ v^2 = 0 + 2 \cdot 0.1 \, \text{m/s}^2 \cdot 2 \, \text{m} \]
Calculating:
\[ v^2 = 0.4 \, \text{m}^2/\text{s}^2 \]
Taking the square root gives:
\[ v = \sqrt{0.4} \approx 0.632 \, \text{m/s} \]

### Step 4: Calculate the kinetic energy (KE)
The formula for kinetic energy is:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values:
\[ KE = \frac{1}{2} \cdot 40 \, \text{kg} \cdot 0.4 \, \text{m}^2/\text{s}^2 \]
Calculating:
\[ KE = 20 \cdot 0.4 = 8 \, \text{J} \]

### Final Answer
The kinetic energy acquired by the body is **8 Joules**.

---