Question

Derive the equation of force by using second law of motion.

Answer 1

Dear Student ,
According to Newton's Second Law of motion the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force .
So , the linear momentum of the body is given by , p = mv
Now , according to Newton,s Second Law of motion ,
Force is directly proportional to the rate of change of momentum
$$\begin{gathered} F\propto \frac{dp}{dt} \\ \Rightarrow F=K\frac{dp}{dt} \\ \Rightarrow F=K\frac{d\left(mv\right)}{dt} \\ \Rightarrow F=Km\frac{dv}{dt} \\ \Rightarrow F=Kma \\ NowexperimentallyK=1 \\ So,F=ma \end{gathered}$$
Which is the required equation .
Regards