//momentum\\
Momentum is just an objects Velocity combined with it's mass, Momentum = mass*Velocity. There isn't much use for it, except when things hit other things. Which is of course the coolest thing about physics
. I'll explain the three types of collisions. First is a perfect collision, where the object hitting the second object becomes part of the second and they both move on at the same speed as the first was initially (likeliness = poor, what with friction and inertia and all that). Second is um, well I forget the name of it, but this is when the first object stops and the second moves on with the first's initial velocity (think pool). The third, imperfect I think, is when both objects travel off in opposite directions in different Velocities.
//Simple Motion\\
Simple motion is the motion of an object in one direction. It deals with Velocity (distance/time), time, distance (or delta(triangle)x, meaning change in x), and acceleration. We use these formulas derived by Galileo in most calculations. Vi and Vf are the initial and final velocities for whatever part of the motion you are looking at.
dist = Vi*time + (1/2)A*time^2
Vf = Vi + A*time
Vf^2 = Vi^2 + 2A*dist
Let's look at the motion of a car going from one stop light to another. The car starts out at 0 m/s, it then accelerates to about 5 m/s (25 mph ?) in 4 meters, he then travels for about 5 seconds then has to accelerate to 0 m/s in 2 meters (didn't see the truck in front stop). How much time, and how far did the car travel? First off, we break this into 3 parts, here's the first part;
The car starts at 0 m/s, and ends up at 5 m/s in 4 meters, so we know Vi, Vf, and dist. We want to know the time and dist, but we already know the distance for this one. So we will want to use the second equation, but we don't know the acceleration so we will use the third to find that first. We then use the calculated acceleration to find the time (this is not recomended since if you use a calculated value to find another value, your values will have a better chance of being wrong, but we didn't have much choice in this situation). Now on to the second;
Now the car is moving at a constant rate, 5 m/s, for 5 seconds. So all we need to know is, how far did the car travel? We use the first equation since it has all of our variables in it. Since acceleration is zero in this case the (1/2)A*time^2 cancels out. So uh, next part;
Now the car has an initial velocity of 5 m/s, final velocity of 0 m/s, and a distance of 2 meters, so we need to find time. We need acceleration this time so we do the same as we did in the first part.
Now we know all the times and distances for each part of the motion, so we just need to add them up to find the answer.
up next - projectile movement, it may take awhile since I'll probably try to explain alot on this...
Edit: forgot about collision types, d'oh!
Edit2: I realized that I screwed up the momentum problem and that what I was trying to show was a bit more complicated than basic physics so I'll leave momentum with the definition and give you simple motion to ease the pain of projectile movement.