# Before a collision, CAR 1 has a mass of 1,200 kg and a velocity of 23 m/s due east and CAR 2 has a mass of 1,400 kg and a velocity of 28 m/s due west. If the two cars experience an completely inelastic collision, what is the final velocity of the two cars?

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

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.