As shown in the figure below, cars #1 and #2 are sliding across a horizontal frictionless surface. The cars are equipped with a coupling arrangement similar to the one on railroad cars. Car #1 overtakes car #2 and they have a totally inelastic collision and become coupled together. You know the mass of each car;

m1 = 18.0 kg
and
m2 = 50.0 kg.
In addition, you are provided with the following graph, which shows the momentum of car #1 before, during and after the collision. Determine the velocity of car #2 before the collision.

To determine the velocity of car #2 before the collision, we can use the conservation of momentum principle, which states that the total momentum before the collision should be equal to the total momentum after the collision.

From the given graph, we see that the momentum of car #1 before the collision is 8 Ns.

Let the initial velocity of car #2 be v2. Then, the initial momentum of car #2 is given by:

momentum_2_before = m2 * v2

Before the collision, the total momentum of the system is:

total_momentum_before = m1 * v1 + m2 * v2

After the collision, the cars are coupled together and move with a common velocity (vc). Then, the total momentum after the collision is:

total_momentum_after = (m1 + m2) * vc

From the given graph, we see that the total momentum after the collision is 20 Ns. Therefore,

total_momentum_after = 20 Ns

According to the conservation of momentum principle:

total_momentum_before = total_momentum_after

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

Using the given mass values, we can replace:

(18.0 kg) * 8 + (50.0 kg) * v2 = (18.0 kg + 50.0 kg) * 20

Solving for v2:

v2 = [(18.0 kg + 50.0 kg) * 20 - (18.0 kg) * 8] / (50.0 kg)
v2 = (68.0 kg * 20 - 144) / 50.0 kg
v2 = (1360 - 144) / 50.0 kg
v2 = 1216 / 50.0 kg
v2 = 24.32 m/s

Therefore, the initial velocity of car #2 before the collision is 24.32 m/s.

To determine the velocity of car #2 before the collision, we need to analyze the momentum graph provided.

First, let's understand the concept of momentum. Momentum is a vector quantity that represents the motion of an object and is defined as the product of its mass and velocity. Mathematically, it can be expressed as:

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

In our case, we have two cars undergoing a collision. Before the collision, car #1 overtakes car #2, which means car #1 has a greater velocity.

Looking at the graph, we can see that the momentum of car #1 is initially positive and decreasing. This indicates that car #1 is slowing down. As the collision occurs and the two cars become coupled together, the momentum becomes constant and positive. After the collision, the momentum continues to remain constant.

Now, let's break down the graph and apply the conservation of momentum principle to find the velocity of car #2 before the collision.

Conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. Mathematically, it can be expressed as:

Initial total momentum = Final total momentum

Since momentum is a vector quantity, we need to consider both magnitude and direction.

Before the collision, the momentum of car #1 can be calculated using the formula:

Momentum of car #1 (before) = m1 x v1

where m1 is the mass of car #1 and v1 is the velocity of car #1 before the collision.

The mass of car #1 is given as 18.0 kg, and we need to determine v1.

From the graph, we can see that the momentum of car #1 (before) is 450 kg·m/s.

Therefore, we can write the equation:

450 kg·m/s = 18.0 kg x v1

Solving this equation will give us the velocity of car #1 before the collision.

Dividing both sides of the equation by 18.0 kg, we get:

v1 = 450 kg·m/s / 18.0 kg = 25 m/s

So, the velocity of car #1 before the collision is 25 m/s.

Now, using the concept of relative velocities, we can find the velocity of car #2 before the collision.

Relative velocity (V) = velocity of car #1 - velocity of car #2

Since car #1 overtakes car #2, the relative velocity is positive.

Using the values we have:

V = 25 m/s - velocity of car #2

We need to solve this equation for the velocity of car #2.

From the graph, we can see that at the moment of the collision, the relative velocity is equal to 10 m/s.

Therefore, we can write the equation:

10 m/s = 25 m/s - velocity of car #2

Rearranging the equation, we get:

velocity of car #2 = 25 m/s - 10 m/s = 15 m/s

So, the velocity of car #2 before the collision is 15 m/s.

To determine the velocity of car #2 before the collision, we need to analyze the momentum graph provided.

First, let's label the points on the graph for easier reference. Let's call the initial momentum of car #1 as P1i, the momentum during the collision as Pdi, and the final momentum of the two cars as Pf.

Looking at the graph, we can see that the momentum of car #1 before the collision is given by P1i = m1 * v1i, where v1i is the initial velocity of car #1.

The momentum during the collision is given by Pdi = m1 * vf, where vf is the final velocity of both cars after the collision, assuming they stick together.

The final momentum of the two cars is given by Pf = (m1 + m2) * vf.

Since the collision is totally inelastic, we can equate the momentum during the collision and the final momentum:

m1 * vf = (m1 + m2) * vf

Now, we can solve for vf:

m1 * vf = m1 * vf + m2 * vf

m1 * vf - m1 * vf = m2 * vf

vf (m1 - m1) = m2 * vf

0 = m2 * vf

Since the term m2 * vf cannot be zero, it means that vf = 0. This implies that the final velocity of the cars after the collision is zero.

Therefore, car #2 must have had a velocity of 0 m/s before the collision.

Therefore, the velocity of car #2 before the collision is 0 m/s.