Question

Show that the rate of change of momentum of an object is the product of its mass and acceleration.

Answer 1

Step 1:- The rate of change of momentum of a body is directly proportional to the applied unbalanced force. The change in momentum is in the direction of this force.

Step 2:- $$\begin{gathered} \Rightarrow Force\propto Rateofchangeofmomentum=\frac{Changeinmomentum}{time} \\ \Rightarrow Force\propto \frac{(Finalmomentum-Initialmomentum)}{time} \\ \Rightarrow F\propto \frac{(mv-mu)}{t} \\ \Rightarrow F\propto \frac{m(v-u)}{t} \\ \Rightarrow F\propto ma \\ \Rightarrow F=kma \\ k=1 \\ \Rightarrow F=ma \end{gathered}$$