Using the equation of newton's second law of motion, derived impulse of a force, show that F=MA where M is mass
Newton's second law of motion states:
F = dp/dt
Where F is the force applied, dp/dt is the rate of change of momentum, and p is the momentum.
Impulse is defined as the integral of force over time:
J = ∫ F dt
Where J is impulse. This can be rewritten as:
J = ∆p
Where ∆p is the change in momentum.
From Newton's second law, we know that force is equal to the rate of change of momentum:
F = dp/dt
Rearranging this equation, we get:
F = ∆p/∆t
Dividing both sides by mass (m), we get:
F/m = ∆p/∆t
Since impulse is equal to change in momentum, we can substitute ∆p for J:
F/m = J/∆t
Since impulse is also equal to force times time:
J = F∆t
Substitute this back into the equation:
F/m = F∆t/∆t
F/m = F
Therefore, F = ma where m is mass.