A formula for before collision

Momentum ($\vec{p}$) is a vector quantity defined as the product of an object's mass ($m$) and its velocity ($\vec{v}$):

$$\vec{p} = m\vec{v}$$

For a system consisting of two objects, object 1 and object 2, the total momentum before a collision is the vector sum of their individual momenta.
Let:

• $m_1$ be the mass of the first object.
• $\vec{v}_{1i}$ be the initial velocity of the first object (before collision).
• $m_2$ be the mass of the second object.
• $\vec{v}_{2i}$ be the initial velocity of the second object (before collision).

The total momentum before the collision ($\vec{P}_{total, i}$) is:

$$\vec{P}_{total, i} = m_1\vec{v}_{1i} + m_2\vec{v}_{2i}$$

This formula is often used as the "before collision" side of the conservation of momentum equation.