A particle of mass $M$ is moving with a uniform velocity $\vec{u}$. It is given an impulse $\vec{J}$

Question

A particle of mass $M$ is moving with a uniform velocity $\vec{u}$. It is given an impulse $\vec{J}$ such that its velocity becomes $\vec{v}$. The relation between $\vec{J}$, $\vec{u}$, and $\vec{v}$ is

Professor PC Thomas Classes · Answer

According to the impulse-momentum theorem, the impulse $\vec{J}$ acting on an object is equal to the change in its linear momentum. Therefore, $\vec{J} = \vec{p}_f - \vec{p}_i = M\vec{v} - M\vec{u} = M(\vec{v} - \vec{u})$.