A collision is an event in which two or more objects exert forces on each other for a short duration of time. It can be either inelastic or elastic collision.

In inelastic collision, some energy is lost. Here, the momentum is conserved but the kinetic energy is lost.

A completely or perfectly inelastic collision is a special case where the two objects stick together and move with a common final velocity after the collision.

The inelastic collision formula is given by:

`m_1v_1+m_2v_2=(m_1+m_2)V`

where

`m_1 ` - mass of object 1

`m_2` - mass of object 2

`v_1` - velocity of object 1

`v_2` - velocity of object 2

`V` - Final velocity of the two objects.

Before the collision, car 1 has a mass `m_1=1200\ kg` with velocity of 23 m/s due east. So, `v_1=23` m/s, and car 2 has a mass `m_2 = 1400\ kg` with velocity of 28 m/s due west. So, `v_2=-28` m/s (since it is in the opposite direction). We have to find the final velocity of the cars after a completely inelastic collision.

Now, according to the formula stated above, we can write,

`(1200 \times 23)+(1400 \times (-28))=(1200+1400)V`

`27600-39200` =`2600V`

`-11600=2600V`

implies `V=-\frac{11600}{2600} = -4.46 ` m/s

So the final velocity of the two cars after a completely inelastic collision is -4.46 m/s.

**Further Reading**

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