An electron starting from rest has a velocity that increases linearly with the time that is v=kt,where k=2 `m//sec^(2)`.The distance travelled in the first 6 seconds will be

Options

A. 9m
B. 16m
C. 27 m
D. 36m

Answer

To solve the problem, we need to find the distance traveled by the electron in the first 6 seconds given that its velocity increases linearly with time according to the equation \( v = kt \), where \( k = 2 \, \text{m/s}^2 \).

### Step-by-Step Solution:

1. **Identify the given values**:
- Initial velocity \( u = 0 \) (the electron starts from rest)
- The equation for velocity \( v = kt \) where \( k = 2 \, \text{m/s}^2 \)
- Time \( t = 6 \, \text{s} \)

2. **Determine the acceleration**:
- Since the velocity increases linearly with time, the acceleration \( a \) is constant and equal to \( k \).
- Therefore, \( a = k = 2 \, \text{m/s}^2 \).

3. **Use the formula for displacement**:
- The formula for displacement when starting from rest is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
- Substituting the known values:
- \( u = 0 \)
- \( a = 2 \, \text{m/s}^2 \)
- \( t = 6 \, \text{s} \)

4. **Calculate the displacement**:
\[ s = 0 \cdot 6 + \frac{1}{2} \cdot 2 \cdot (6^2) \]
\[ s = 0 + \frac{1}{2} \cdot 2 \cdot 36 \]
\[ s = 1 \cdot 36 = 36 \, \text{m} \]

5. **Conclusion**:
- The distance traveled by the electron in the first 6 seconds is \( 36 \, \text{m} \).

### Final Answer:
The distance traveled in the first 6 seconds is **36 meters**.