A 2.0 kg lab car moving to the right with an initial velocity of 3.0 m/s collides with a 1.0 kg lab car moving to the left with a velocity of 8.0 m/s in a inelastic collision. What us the final velocity?

Take left to be negative.

inelastic means the cars stick together

momentum is conserved

(2.0 * 3.0) - (1.0 * 8.0) = (2.0 + 1.0) * v

To find the final velocity of the system after the inelastic collision, we can use the law of conservation of momentum.

The law of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. In this case, the system consists of the two lab cars.

The equation for conservation of momentum can be written as:

(m1 * v1) + (m2 * v2) = (m1 + m2) * vf

Where:
m1 = mass of the first car = 2.0 kg
v1 = initial velocity of the first car = 3.0 m/s
m2 = mass of the second car = 1.0 kg
v2 = initial velocity of the second car = -8.0 m/s (since left is negative)
vf = final velocity of the system

Plugging in the values, we get:

(2.0 kg * 3.0 m/s) + (1.0 kg * -8.0 m/s) = (2.0 kg + 1.0 kg) * vf

(6.0 kg m/s) + (-8.0 kg m/s) = (3.0 kg) * vf

-2.0 kg m/s = 3.0 kg * vf

Dividing both sides by 3.0 kg, we get:

-2.0 kg m/s / 3.0 kg = vf

vf = -0.67 m/s

Therefore, the final velocity of the system after the inelastic collision is -0.67 m/s.

To find the final velocity of the system after the collision, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

Momentum is defined as the product of mass and velocity. So, we need to calculate the initial momentum and the final momentum, and then equate them.

First, let's determine the initial momentum of the system. The momentum of an object is given by the formula:

Momentum = mass × velocity

For the first car (2.0 kg) moving to the right with an initial velocity of 3.0 m/s, the momentum is:

Momentum1 = mass1 × velocity1
= 2.0 kg × 3.0 m/s
= 6.0 kg·m/s (to the right)

For the second car (1.0 kg) moving to the left with a velocity of -8.0 m/s (negative because it's moving to the left), the momentum is:

Momentum2 = mass2 × velocity2
= 1.0 kg × (-8.0 m/s)
= -8.0 kg·m/s (to the left)

Now, let's consider the final momentum of the system after the collision. Since the collision is inelastic, the two cars will stick together and move as one mass after the collision. Let's denote the final velocity of the combined system as v.

The final momentum is given by:

Momentum_final = (mass1 + mass2) × v

Using the conservation of momentum principle, we set the initial momentum equal to the final momentum:

Momentum1 + Momentum2 = Momentum_final

6.0 kg·m/s + (-8.0 kg·m/s) = (2.0 kg + 1.0 kg) × v

-2.0 kg·m/s = 3.0 kg × v

Now, solve for v:

v = -2.0 kg·m/s / 3.0 kg
v ≈ -0.67 m/s

Therefore, the final velocity after the collision is approximately -0.67 m/s, considering left to be negative.