Impulse,  $\overrightarrow{J}={\displaystyle {\int }_{t_1}^{t_2}\overrightarrow{F}.dt}$

or            $J=F_{\mathrm{avg}}.\Delta t$

Now, according to Newton’s Second Law

 $\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}\mathrm{or}{\displaystyle {\int }_{t_1}^{t_2}\overrightarrow{F}.dt}={\displaystyle {\int }_{{\overrightarrow{P}}_1}^{{\overrightarrow{P}}_2}d\overrightarrow{P}}$

 $\therefore \overrightarrow{J}={\overrightarrow{P}}_2-{\overrightarrow{P}}_1=\Delta \overrightarrow{P}$  

[i.e., the action of impulse is to change  the momentum of a body and the impulse of force is equal to the change in momentum. This is also known as impulse-momentum theorem]

In the given case,

Impulse  $={\overrightarrow{p}}_2-{\overrightarrow{p}}_1$  
 (i.e., impulse  $=$ change in momentum)

or Impulse,  $J=M{\overrightarrow{v}}_2-M{\overrightarrow{v}}_1$

 $\begin{array}{l}\Rightarrow J=M\left[\left(v\right)-(-v)\right]\\ \Rightarrow J=2Mv\mathrm{N} \mathrm{s}\end{array}$