Force of 4 N is applied on a body of mass 20 kg. The work done in 3rd second is

Options

A. 2 J
B. 4 J
C. 16 J
D. 1.2 J

Explanation

To solve the problem of finding the work done on a body in the third second when a force of 4 N is applied to a mass of 20 kg, we can follow these steps:

### Step 1: Calculate the acceleration of the body
Using Newton's second law of motion, we can find the acceleration (a) of the body using the formula:
\[ F = m \cdot a \]
Where:
- \( F \) is the force applied (4 N)
- \( m \) is the mass of the body (20 kg)

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{4 \, \text{N}}{20 \, \text{kg}} = \frac{4}{20} = \frac{1}{5} \, \text{m/s}^2 \]

### Step 2: Find the distance traveled in the third second
The distance traveled in the nth second can be calculated using the formula:
\[ s_n = u + \frac{1}{2} a (2n - 1) \]
Where:
- \( s_n \) is the distance traveled in the nth second
- \( u \) is the initial velocity (0 m/s, since the body starts from rest)
- \( a \) is the acceleration (1/5 m/s²)
- \( n \) is the second for which we want to find the distance (3)

Substituting the values into the formula:
\[ s_3 = 0 + \frac{1}{2} \cdot \frac{1}{5} \cdot (2 \cdot 3 - 1) \]
Calculating:
\[ s_3 = \frac{1}{2} \cdot \frac{1}{5} \cdot (6 - 1) \]
\[ s_3 = \frac{1}{2} \cdot \frac{1}{5} \cdot 5 \]
\[ s_3 = \frac{1}{2} \, \text{m} \]

### Step 3: Calculate the work done in the third second
The work done (W) can be calculated using the formula:
\[ W = F \cdot s \]
Where:
- \( W \) is the work done
- \( F \) is the force applied (4 N)
- \( s \) is the distance traveled in the third second (1/2 m)

Substituting the values:
\[ W = 4 \, \text{N} \cdot \frac{1}{2} \, \text{m} \]
Calculating:
\[ W = 2 \, \text{J} \]

### Final Answer
The work done in the third second is **2 Joules**.

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