How do you calculate the velocity after a collision?

To calculate the velocity after a collision, you can use the principles of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision. This can be expressed with the formula ( m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f} ), where ( m ) represents mass, ( v_i ) is the initial velocity, and ( v_f ) is the final velocity of each object involved in the collision. Depending on whether the collision is elastic or inelastic, you may also need to consider kinetic energy conservation for elastic collisions.