A body of mass 5kg initially at rest, is subjected to a force of 40 N. Find the kinetic energy acquired by the body at the end of 5 seconds :

Options

A. 4000 J
B. 6000 J
C. 6249 J
D. 6145 N

Answer

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

### Step 1: Identify the given values
- Mass of the body (m) = 5 kg
- Initial velocity (u) = 0 m/s (since the body is initially at rest)
- Force (F) = 40 N
- Time (t) = 5 s

### Step 2: Calculate the acceleration of the body
Using Newton's second law of motion, we can calculate the acceleration (a) using the formula:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{40 \, \text{N}}{5 \, \text{kg}} = 8 \, \text{m/s}^2 \]

### Step 3: Calculate the final velocity after 5 seconds
We can use the equation of motion to find the final velocity (v) after time t:
\[ v = u + at \]

Substituting the values:
\[ v = 0 + (8 \, \text{m/s}^2)(5 \, \text{s}) = 40 \, \text{m/s} \]

### Step 4: Calculate the kinetic energy acquired by the body
The formula for kinetic energy (KE) is:
\[ KE = \frac{1}{2} mv^2 \]

Substituting the values:
\[ KE = \frac{1}{2} \times 5 \, \text{kg} \times (40 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 5 \times 1600 \]
\[ KE = \frac{1}{2} \times 8000 \]
\[ KE = 4000 \, \text{J} \]

### Final Answer
The kinetic energy acquired by the body at the end of 5 seconds is **4000 Joules**.

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