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

A particle of mass m is moving with a uniform velocity v1. It is given an impulse such that its velocity becomes v2. The impulse is equal to 

\[{(a)}\quad m \left[ |v_2| - |v_1| \right] \] \[{(b)}\quad \frac{1}{2} m \left[ v_2^2 - v_1^2 \right] \] \[{(c)}\quad m \left[ v_1 + v_2 \right]\] \[{(d)}\quad m \left[ v_2 - v_1 \right]\]

[NEET 1990]

\[ F = \frac{m\vec{v} - m\vec{u}}{\Delta t} \] Impulse,\[ F \cdot \Delta t = m\vec{v} - m\vec{u} \] \[ = m(\vec{v} - \vec{u}) \] \[ = m(\vec{v_2} - \vec{v_1}) \]

Note that Impulse and Change in momentum are vector quantity, not scalar. So Option (d).