A particle of mass $$m$$ is moving with a uniform velocity $${v_1}.$$ It is given an impulse such that its velocity becomes $${v_2}.$$ The impulse is equal to

Solution :
Impulse of a force can be calculated as the product of large force applied to the small time to which force act.
$$\eqalign{ & {\text{i}}{\text{.e}}{\text{.}}\,\,F = \frac{{dp}}{{dt}} \cr & \Rightarrow F \cdot dt = dp \cr & \Rightarrow {\text{impulse}} = {p_2} = {p_1} \cr} $$
Impulse of a force, which is the product of average force during impact and the time for which the impact lasts, is measured by the total change in linear momentum produced during the impact.
Here, $${p_1} = m{v_1},{p_2} = m{v_2}$$
Impulse, $$I = m{v_2} - m{v_1} = m\left( {{v_2} - {v_1}} \right)$$