We can derive Newton's

Options

A. second and third laws from the first law.
B. first and second laws from the first law.
C. third and first laws from the second law.
D. all the three laws are independent of each other.

Explanation

To derive the relationships between Newton's three laws of motion, we can follow a systematic approach. Here’s a step-by-step solution:

### Step 1: Understanding Newton's Laws
- **Newton's First Law** states that an object at rest will remain at rest, and an object in motion will continue in motion with the same speed and in the same direction unless acted upon by a net external force.
- **Newton's Second Law** states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it is expressed as \( F = ma \) (where \( F \) is the net force, \( m \) is mass, and \( a \) is acceleration).
- **Newton's Third Law** states that for every action, there is an equal and opposite reaction. This means that if body A exerts a force on body B, then body B exerts a force of equal magnitude and opposite direction on body A.

### Step 2: Deriving the First Law from the Second Law
- From the Second Law, if the net force \( F \) acting on an object is zero, then the acceleration \( a \) is also zero (since \( F = ma \)).
- If \( a = 0 \), the object remains in its state of rest or uniform motion. This is essentially the statement of the First Law.

### Step 3: Deriving the Third Law from the Second Law
- Consider two bodies, A and B. Let body A exert a force \( F_1 \) on body B, and body B exert a force \( F_2 \) on body A.
- According to the Second Law, the change in momentum of body A due to force \( F_1 \) is given by \( \Delta P_A = F_1 \Delta t \) and for body B, it is \( \Delta P_B = F_2 \Delta t \).
- If there are no external forces acting on the system of A and B, the total change in momentum of the system must be zero. Therefore, \( F_1 \Delta t + F_2 \Delta t = 0 \).
- This implies \( F_1 = -F_2 \), which is the statement of the Third Law.

### Step 4: Conclusion
- We have shown that:
- The First Law can be derived from the Second Law.
- The Third Law can also be derived from the Second Law.
- Thus, the Second Law is fundamental because it allows us to derive both the First and Third Laws.

### Final Answer
The correct relationship is that the First and Third Laws can be derived from the Second Law, making the Second Law the "real law" of motion.