A constant force `(F)` is applied on a stationary particle of mass 'm' The velocity attained by the particle in a certain displacement will be proportional to .

Options

A. m
B. `1//m`
C. `sqrtm`
D. `(1)/sqrtm`

Answer

To solve the problem, we need to determine how the velocity attained by a stationary particle of mass 'm' under the influence of a constant force 'F' is related to the displacement.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- A constant force \( F \) is applied to a stationary particle of mass \( m \).
- The initial velocity \( u = 0 \) (since the particle is stationary).

2. **Use Newton's Second Law of Motion**:
- According to Newton's second law, the acceleration \( a \) of the particle can be expressed as:
\[ a = \frac{F}{m} \]

3. **Apply the Kinematic Equation**:
- We can use the kinematic equation that relates velocity, initial velocity, acceleration, and displacement:
\[ v^2 = u^2 + 2as \]
- Substituting \( u = 0 \) and \( a = \frac{F}{m} \):
\[ v^2 = 0 + 2 \left(\frac{F}{m}\right) s \]
- This simplifies to:
\[ v^2 = \frac{2Fs}{m} \]

4. **Solve for Velocity \( v \)**:
- Taking the square root of both sides gives:
\[ v = \sqrt{\frac{2Fs}{m}} \]

5. **Identify the Proportionality**:
- From the equation \( v = \sqrt{\frac{2Fs}{m}} \), we can see that the velocity \( v \) is proportional to the square root of the displacement \( s \) when \( F \) and \( m \) are constants:
\[ v \propto \sqrt{s} \]

### Conclusion:
The velocity attained by the particle in a certain displacement will be proportional to \( \sqrt{s} \).