How would I graph a collision. i.e if I have a problem

A 12,000 kg railroad car traveling at a speed of 19 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?

What would my x axis be and what would my y axis be ?

They are not asking you to graph the collision. All you need to do is apply a momentum conservation formula to compute a final speed.

The final speed is half the initial speed of the moving car.

To graph the collision scenario, you would need to use a position vs. time graph. Here's how you can do it:

1. Determine the time range for the graph: Since we are interested in the common speed of the cars after the collision, you can choose a time range that covers the period from before the collision to after the cars lock together. Let's assume a time range of 0 to t seconds.

2. Determine the position values for each car: Since the cars are moving on a straight line, we can assume the position of the cars before the collision as -x1 for the moving car (12,000 kg) and 0 for the stationary car. After the collision, when the cars lock together, the position of both cars will be the same. You can represent this position as -x2.

3. Plot the graph: On the x-axis, represent time (t). On the y-axis, represent position (x). For the moving car (12,000 kg) before the collision, plot a straight line from position -x1 at time 0, moving linearly upward as time progresses. For the stationary car, plot a horizontal line at position 0. After the collision, when the cars lock together, both lines should merge into a single line representing position -x2.

To find the common speed of the cars after the collision, you don't need to graph it. Instead, you can use the principles of conservation of momentum. Assuming no external forces act on the system, the sum of the momentum before the collision should be equal to the sum of the momentum after the collision.

Let the initial velocity of the moving car be v1 and the final velocity (common velocity) of the cars after the collision be v2.

Conservation of momentum equation:
(moving car mass * v1) + (stationary car mass * 0) = (combined mass * v2)

Substituting the given values:
(12,000 kg * 19 m/s) + (12,000 kg * 0) = (24,000 kg * v2)

Simplifying the equation, you can solve for v2, which will give you the common speed of the cars after the collision.