two equal mass cars collide head to tail and their bumpers lock. One car has a velocity of 10m/s and the other is at rest. what is the velocity of the two cars after the collision?

initial momentum = 10 m + 0 = 10 m

so final momentum = 10 m
so
m v + m v = 10 m
2 v = 10
v = 5

To find the velocities of the two cars after the collision, we can apply the principle of conservation of momentum.

The formula for momentum is:

p = m * v

where p is momentum, m is mass, and v is velocity.

In this case, since the masses of the two cars are equal, we can simplify the equation to:

p1 + p2 = 0

Initially, only Car 1 has momentum, as Car 2 is at rest. Let's denote the mass as m and the initial velocity of Car 1 as v1.

So, p1 = m * v1

After the collision, the cars lock bumpers, and they will move together as one system. Therefore, the velocities of the two cars will be equal. Let's denote the final velocity of the two cars as v'.

So, the momentum after the collision is:

p1' + p2' = (2m) * v'

Since the principle of conservation of momentum states that the total momentum before the collision should equal the total momentum after the collision, we can set up the following equation:

p1 + p2 = p1' + p2'

m * v1 + 0 = (2m) * v'

Now, substituting the given values:

m * 10 + 0 = (2m) * v'

10m = 2m * v'

Dividing both sides by 2m:

10/2 = v'

v' = 5 m/s

Therefore, the velocity of both cars after the collision is 5 m/s.

To determine the velocity of the two cars after the collision, we can apply the principles of conservation of momentum.

The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided that no external forces are acting on the system.

Momentum is defined as the product of mass and velocity:
Momentum = mass × velocity

In this case, the two cars have the same mass, so we can denote their masses as m. The velocity of the first car is 10 m/s and the second car is at rest, so its velocity is 0 m/s.

Before the collision, the total momentum is:
Initial momentum = (mass of first car × velocity of first car) + (mass of second car × velocity of second car)
Initial momentum = (m × 10 m/s) + (m × 0 m/s)
Initial momentum = 10m

Since the cars are initially at rest vertically (one bumper is attached to the other), the total momentum is conserved horizontally.

After the collision, the two cars move together with the same velocity, denoted as v. Thus, the total momentum after the collision is:
Final momentum = (mass of combined cars × velocity of combined cars)
Final momentum = (2m × v)

Using the principle of conservation of momentum, we equate the initial and final momenta:
Initial momentum = Final momentum
10m = 2mv

Dividing both sides of the equation by 2m, we get:
10m / (2m) = 2mv / (2m)
5 = v

Therefore, the velocity of the two cars after the collision is 5 m/s, and they move together in the same direction.