A body of mass `5 kg` at rest under the action of a force which gives its velocity given by `v = 3 xx t m//s`, here 't' is time in seconds. The work done by the force in two seconds will be

Options

A. 90 J
B. 45 J
C. 180 J
D. 30 J

Explanation

To solve the problem of finding the work done by the force on a body of mass 5 kg over 2 seconds, we can follow these steps:

### Step 1: Identify the given information
- Mass of the body (m) = 5 kg
- Velocity as a function of time (v) = 3t m/s
- Time (t) = 2 seconds

### Step 2: Find the acceleration
The velocity function is given as \( v = 3t \). To find the acceleration, we differentiate the velocity with respect to time:
\[ a = \frac{dv}{dt} = \frac{d(3t)}{dt} = 3 \, \text{m/s}^2 \]

### Step 3: Calculate the force acting on the body
Using Newton's second law, the force (F) can be calculated as:
\[ F = m \cdot a = 5 \, \text{kg} \cdot 3 \, \text{m/s}^2 = 15 \, \text{N} \]

### Step 4: Calculate the final velocity at t = 2 seconds
Substituting \( t = 2 \) seconds into the velocity equation:
\[ v = 3 \cdot 2 = 6 \, \text{m/s} \]

### Step 5: Calculate the displacement in 2 seconds
Using the kinematic equation:
\[ v^2 = u^2 + 2as \]
where \( u \) (initial velocity) = 0 (since the body starts from rest), \( v = 6 \, \text{m/s} \), and \( a = 3 \, \text{m/s}^2 \):
\[ 6^2 = 0 + 2 \cdot 3 \cdot s \]
\[ 36 = 6s \]
\[ s = \frac{36}{6} = 6 \, \text{m} \]

### Step 6: Calculate the work done
The work done (W) by the force is given by:
\[ W = F \cdot s = 15 \, \text{N} \cdot 6 \, \text{m} = 90 \, \text{J} \]

### Final Answer
The work done by the force in two seconds is **90 Joules**.

---