A body of mass 2kg at rest is supplied constant power 1J/sec, the distance travelled by body after 6 sec is

Options

A. `2sqrt6` m
B. `4sqrt m`
C. 2 sqrt3 m`
D. 6 sqrt3 m`

Answer

To solve the problem of finding the distance traveled by a body of mass 2 kg under constant power of 1 J/s after 6 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- Mass of the body, \( m = 2 \, \text{kg} \)
- Initial velocity, \( u = 0 \, \text{m/s} \) (the body is at rest)
- Power supplied, \( P = 1 \, \text{J/s} \)
- Time, \( t = 6 \, \text{s} \)

2. **Using the Work-Energy Theorem:**
The work done on the body is equal to the change in kinetic energy:
\[ W = \Delta K \]
The work done can also be expressed in terms of power:
\[ W = P \cdot t \]
Therefore, we can write:
\[ P \cdot t = \Delta K \]

3. **Calculating Work Done:**
Substitute the values of power and time:
\[ W = 1 \, \text{J/s} \cdot 6 \, \text{s} = 6 \, \text{J} \]

4. **Finding the Change in Kinetic Energy:**
The change in kinetic energy is given by:
\[ \Delta K = \frac{1}{2} m v^2 - \frac{1}{2} m u^2 \]
Since the initial velocity \( u = 0 \):
\[ \Delta K = \frac{1}{2} m v^2 \]
Setting this equal to the work done:
\[ 6 = \frac{1}{2} \cdot 2 \cdot v^2 \]
Simplifying gives:
\[ 6 = v^2 \]
Therefore:
\[ v = \sqrt{6} \, \text{m/s} \]

5. **Finding the Distance Traveled:**
The distance traveled under constant acceleration can be found using the formula:
\[ s = ut + \frac{1}{2} a t^2 \]
Since the body starts from rest, \( u = 0 \). We need to find the acceleration \( a \):
\[ P = F \cdot v \implies F = \frac{P}{v} = \frac{1}{\sqrt{6}} \, \text{N} \]
Using Newton's second law:
\[ F = m \cdot a \implies a = \frac{F}{m} = \frac{1/\sqrt{6}}{2} = \frac{1}{2\sqrt{6}} \, \text{m/s}^2 \]

6. **Calculating the Distance:**
Now substituting \( a \) into the distance formula:
\[ s = 0 + \frac{1}{2} \left(\frac{1}{2\sqrt{6}}\right) (6^2) = \frac{1}{2} \cdot \frac{1}{2\sqrt{6}} \cdot 36 \]
Simplifying gives:
\[ s = \frac{18}{\sqrt{6}} = 3\sqrt{6} \, \text{m} \]

### Final Result:
The distance traveled by the body after 6 seconds is:
\[ s = 3\sqrt{6} \, \text{meters} \]