Momentum
The momentum of a particle is defined as the product of the particle mass and the particle velocity as follows:
[tex]\overrightarrow{p}=m\overrightarrow{v}[/tex]
On the other hand, the impulse of a constant force is defined as:
[tex]\overrightarrow{J}=\varSigma\overrightarrow{F}(t_{2}-t_{1})=\varSigma\overrightarrow{F}\Delta t[/tex]
We also know that the net force acting on a particle equals the rate of change of the particle’s momentum, so:
[tex]\varSigma\overrightarrow{F}=m\overrightarrow{a}=m\frac{d}{dt}(\overrightarrow{v})=\frac{d}{dt}(m\overrightarrow{v})=\frac{d\overrightarrow{p}}{dt}[/tex]
If the force is constant, then [tex]\frac{d\overrightarrow{p}}{dt}[/tex] equals the total change in momentum over a period of time:
[tex]\varSigma\overrightarrow{F}=\frac{\overrightarrow{p_{2}}-\overrightarrow{p_{1}}}{t_{2}-t_{1}} \\ \\ \varSigma\overrightarrow{F}(t_{2}-t_{1})=\overrightarrow{p_{2}}-\overrightarrow{p_{1}} \\ \\ \boxed{\overrightarrow{J}=\Delta \overrightarrow{p}}[/tex]
