I've been assigned with a lab to do for my physics class, so my answers have to be based on empirical evidence that I collected myself. The objective is to find the average force of friction that acts on 2 cars as they move towards one another on a flat table, collide, and bounce back in opposite directions. No series of steps were given to me - I have to find out how to do this on my own.

So during class, I had to collect my data. I had 2 cars that could be put on this rail-like track to ensure that they moved in a straight line towards each other. There were motion sensors set up to find the speed of each car in certain time intervals. The 2 cars were on the track, apart from each other, and all I had to do was push them towards each other, one with each hand, trying my best to push both cars at around the same time. They collided, bouncing back in opposite directions, and the motion sensors basically did my data collection for me. Pretty simple. There were also some small magnets on the ends of the cars (on the sides that were facing each other) that repelled one another, so there was a bit of extra force coming from that repulsion when the cars collided and bounced back.

So I used a scale to find the mass of both cars, so I have that info, as well as the time during which they were travelling and collided with each other, and their displacement and speed at certain time intervals. My teacher told me that I am not allowed to use acceleration in my calculations at all. It is supposed to be based on the concept of momentum. Another hint that was given is that graphical analysis techniques might come in handy (like manipulating a variable in a graph to get a straight line to see how they're proportional to each other), but this just left me confused.

So I'm pretty stumped on this. First of all, we haven't learned about magnets yet so I'm assuming that any extra force coming from the magnets is going to be ignored and just considered as a source of error in the lab. The track is very smooth - there was extremely little change in the speeds of the cars as they moved towards each other, but granted, their displacement wasn't that great. I had to push them towards each other with my hands so I just stretched my arms as far apart as I could, holding one car in each hand, then pushed them towards each other. I think the system should be the 2 cars, which means that friction is an external force, so momentum isn't conserved so I can't use those equations. I'm not really sure about the elasticity of the collision - I mean, technically, kinetic energy should have been lost upon collision so they should be slower when they bounce back than when they were going towards each other, but the magnets also provide an extra push when they bounce back. Is this even relevant? :/ I don't know.

I know that net force = change in momentum/time. This is the equation I'm currently planning to use. Another idea I have at the moment is using energy - the work done by friction will be equal to the change in mechanical energy, which is just the difference in kinetic energy since the gravitational potential energy is the same the whole time (the desk is level and flat). But I'm just unsure of so many things. Would I have to consider both static friction and kinetic friction because the cars have to overcome static friction just before they start moving, or is that not even relevant? Am I right in disregarding the magnetic forces? And what does my teacher's hint (of using graphical manipulation techniques) have to do with anything? Any help would be greatly appreciated.