In the following simulation you can change the masses of both carts and the starting velocity of cart A. You can also decide which type of equation by setting the value of e. If e is a decimal between 0 and 1, it is inelastic. If e = 0, then the collision will be perfectly inelastic.

Note in the simulation they use the following variables:

simulation	mA	mb	uA	uB	VA	VB
this lesson	m1	m2	v1i	v2i	v1f	v2f

Copy the following chart, and then run the collisions in the animation and record the values. Plug the m_A, m_B, u_A, u_B, v_A, and v_B into the collision equation, and record the values of right and left sides of the equation in the table to check if they are equal.

If two objects start out together and then push off from one another, or if one object breaks into two pieces that move apart; physicists call it an explosion. This is like a perfectly inelastic collision in reverse, and the equation looks very similar:

(m₁ + m₂) v_i = m₁v_1f + m₂ v_2f

The classic physics example is:
Two students standing together on roller skates push off from one another. If the 60 kg student moves to the left at 3 m/s, how fast will the 90 kg student be moving?

Given: m₁ = 60 kg    m₂ = 90 kg    v_i = 0 m/s    v_1f = -3 m/s (left = negative)
Unknown: v_2f = ?
Equation: (m₁ + m₂)v_i = m_iv_1f + m₂v_2f
Simplify: vi = 0 m/s, so the equation becomes:     0 = m₁v_1f + m₂v_2f or -m₁v_1f = m₂v_2f

Solve: -m₁v_1f = m₂v_2f
-(60)(-3) = 90v_2f
180 = 90v_2f
2 = v_2f
v_2f = 2 m/s