An automobile has a mass of 2000 kg and a velocity of +12 m/s. It makes a rear-end collision with a stationary car whose mass is 1850 kg. The cars lock bumpers and skid off together with the wheels locked.

and the question?

2000N box that has an area of 40m^2

To determine the final velocity of the cars after the collision, we need to apply the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.

Momentum is calculated by multiplying the mass of an object by its velocity. The momentum of an object can be represented by the equation:

Momentum (p) = mass (m) * velocity (v)

Let's calculate the initial momentum of each car:

Car 1 (moving car):
Mass (m1) = 2000 kg
Velocity (v1) = +12 m/s
Momentum (p1) = m1 * v1 = 2000 kg * 12 m/s = 24000 kg·m/s

Car 2 (stationary car):
Mass (m2) = 1850 kg
Velocity (v2) = 0 m/s (since it is stationary)
Momentum (p2) = m2 * v2 = 1850 kg * 0 m/s = 0 kg·m/s

The total initial momentum before the collision is the sum of the individual momenta of each car:

Total initial momentum = p1 + p2 = 24000 kg·m/s + 0 kg·m/s = 24000 kg·m/s

During the collision, the cars lock bumpers and skid off together with locked wheels. This means that their final velocities after the collision will be the same.

Let's represent the final velocity of the cars as "vf". Since the cars move together, their total momentum after the collision will be:

Total momentum after collision = (m1 + m2) * vf

According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision:

Total initial momentum = Total momentum after collision

24000 kg·m/s = (2000 kg + 1850 kg) * vf

Simplifying the equation:

24000 kg·m/s = 3850 kg * vf

Dividing both sides of the equation by 3850 kg:

6.23 m/s = vf

Therefore, the final velocity of the cars after the collision is approximately 6.23 m/s.