Substitution mv+mv=(m+m)v

The principle is the conservation of linear momentum, which states that in a closed system, the total momentum before an event (like a collision) is equal to the total momentum after the event.

• m: mass
• v: velocity
• mv: momentum (mass × velocity)
• The equation shows the sum of the initial momenta of two objects (m₁v₁ + m₂v₂) equaling the final momentum of a combined mass (m₁ + m₂) moving at a final velocity (v_f).

Let the initial velocities be v₁ and v₂. The equation becomes:
m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

This specific form, mv + mv = (m+m)v, implies two objects of equal mass (let's call it 'm') are colliding and sticking together (a perfectly inelastic collision). The first 'mv' represents the momentum of the first object, and the second 'mv' represents the momentum of the second object. After the collision, their masses add up (m+m), and they move with a single final velocity 'v'.

The equation is a direct application of the conservation of momentum for a specific case of two equal masses colliding inelastically.