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 steps:

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

### Step 2: Calculate the acceleration using Newton's second law
According to Newton's second law, the force is equal to mass times acceleration (F = ma). We can rearrange this to find acceleration (a):
\[ a = \frac{F}{m} \]
Substituting the known values:
\[ a = \frac{40 \, \text{N}}{5 \, \text{kg}} = 8 \, \text{m/s}^2 \]

### Step 3: Calculate the final velocity after 5 seconds
Using the formula for final velocity when starting from rest:
\[ v = u + at \]
Substituting the known 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 kinetic energy (KE) can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
Substituting the values we have:
\[ KE = \frac{1}{2} (5 \, \text{kg}) (40 \, \text{m/s})^2 \]
Calculating the square of the velocity:
\[ 40^2 = 1600 \]
Now substituting this back into the kinetic energy formula:
\[ KE = \frac{1}{2} (5) (1600) = \frac{8000}{2} = 4000 \, \text{Joules} \]

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

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