A constant force (F) is applied on a stationary particle of mass m, the velocity attained by the particle in a certain interval of time will be proportional to

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a stationary particle of mass \( m \) and a constant force \( F \) is applied to it. We need to find out how the velocity \( v \) of the particle after a certain time \( t \) is related to the mass \( m \).

2. **Applying Newton's Second Law**: According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
\[ F = m \cdot a \]
Rearranging this gives us the acceleration \( a \):
\[ a = \frac{F}{m} \]

3. **Using Kinematic Equation**: We will use the kinematic equation that relates initial velocity, final velocity, acceleration, and time:
\[ v = u + a \cdot t \]
Here, \( u \) is the initial velocity. Since the particle is initially stationary, \( u = 0 \). Thus, the equation simplifies to:
\[ v = a \cdot t \]

4. **Substituting for Acceleration**: Now substituting the expression for acceleration \( a \) from step 2 into the kinematic equation:
\[ v = \left(\frac{F}{m}\right) \cdot t \]

5. **Final Expression**: This gives us:
\[ v = \frac{F \cdot t}{m} \]
From this equation, we can see that the velocity \( v \) is inversely proportional to the mass \( m \) when force \( F \) and time \( t \) are constant.

### Conclusion:
The velocity attained by the particle is proportional to \( \frac{1}{m} \).