Newton's second law of motion is

Options

A. 1. `F=(dp)/(dt)`
B. 2. F=mv
C. 3. `F=mv^(2)`
D. 4. `F=m^(2)v`

Explanation

To solve the question regarding Newton's second law of motion, we can break it down step by step:

### Step 1: Understanding Momentum
Momentum (p) is defined as the product of mass (m) and velocity (v) of an object. Mathematically, it is expressed as:
\[ p = m \cdot v \]

### Step 2: Rate of Change of Momentum
The rate of change of momentum refers to how quickly the momentum of an object changes over time. This can be expressed as:
\[ \frac{dp}{dt} \]
where \( dp \) is the change in momentum and \( dt \) is the change in time.

### Step 3: Newton's Second Law Statement
Newton's second law states that the rate of change of momentum of an object is directly proportional to the net force (F) acting on it. This can be mathematically represented as:
\[ \frac{dp}{dt} \propto F \]

### Step 4: Introducing the Proportionality Constant
To convert the proportionality into an equation, we introduce a constant of proportionality (k):
\[ \frac{dp}{dt} = k \cdot F \]

### Step 5: Determining the Value of k
Through experimental observations, it has been determined that the value of k is equal to 1 in the SI unit system. Therefore, we can simplify the equation to:
\[ \frac{dp}{dt} = F \]

### Step 6: Conclusion
Thus, Newton's second law of motion can be summarized as:
\[ F = \frac{dp}{dt} \]
This means that the net force acting on an object is equal to the rate of change of its momentum.