Prove that the rate of change of linear momentum of a body is equal to the net force acting on thebody

Sure, here is the step by step proof:

1. The linear momentum of a body is given by the product of its mass and velocity. It is represented as P = mv, where P is the momentum, m is the mass and v is the velocity.

2. The rate of change of momentum is given by the derivative of momentum with respect to time. It is represented as dP/dt = m dv/dt + v dm/dt.

3. According to Newton's second law of motion, the force acting on a body is equal to the mass of the body times the acceleration of the body. It is represented as F = ma, where F is the force and a is the acceleration.

4. Acceleration is the rate of change of velocity with respect to time. It is represented as a = dv/dt.

5. Substituting a = dv/dt in F = ma, we get F = m dv/dt.

6. In most cases, the mass of a body remains constant. So, dm/dt = 0.

7. Substituting dm/dt = 0 in dP/dt = m dv/dt + v dm/dt, we get dP/dt = m dv/dt.

8. Comparing F = m dv/dt and dP/dt = m dv/dt, we can see that F = dP/dt.

Therefore, the rate of change of linear momentum of a body is equal to the net force acting on the body.