According to Newton second law of motion

Options

A. `F=m times v`
B. `f= m times a`
C. `f=m/a`
D. `f=m/v`

Explanation

**Step-by-Step Solution:**

1. **Understanding Newton's Second Law of Motion**:
Newton's second law states that the force acting on an object is equal to the rate of change of its momentum. Mathematically, this can be expressed as:
\[ F \propto \frac{dP}{dt} \]
where \( F \) is the force, \( P \) is the momentum, and \( t \) is time.

2. **Converting Proportionality to Equality**:
To convert the proportionality into an equality, we introduce a constant of proportionality. In this case, we can express it as:
\[ F = k \cdot \frac{dP}{dt} \]
By convention, we take \( k = 1 \), leading to:
\[ F = \frac{dP}{dt} \]

3. **Expressing Momentum**:
The momentum \( P \) of an object is defined as the product of its mass \( m \) and its velocity \( v \):
\[ P = mv \]
Therefore, the change in momentum can be expressed as:
\[ \Delta P = P_2 - P_1 = mv_2 - mv_1 \]

4. **Calculating Rate of Change of Momentum**:
The rate of change of momentum with respect to time is given by:
\[ \frac{dP}{dt} = \frac{P_2 - P_1}{t} = \frac{mv_2 - mv_1}{t} \]

5. **Substituting into the Force Equation**:
Substituting the expression for the rate of change of momentum into the force equation gives:
\[ F = \frac{mv_2 - mv_1}{t} \]

6. **Simplifying the Expression**:
Factoring out the mass \( m \) from the equation:
\[ F = m \cdot \frac{(v_2 - v_1)}{t} \]
The term \( \frac{(v_2 - v_1)}{t} \) represents acceleration \( a \):
\[ F = ma \]

7. **Conclusion**:
Thus, the mathematical statement of Newton's second law of motion is:
\[ F = ma \]
This indicates that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

8. **Choosing the Correct Option**:
Based on the derived equation \( F = ma \), we can conclude that the correct option is the one that states \( F = ma \).

---