I'm writing this because loads of people on the forums ask for how to do stuff, like distances. Well I'll try to cover as much as I can in this article. If I miss anything, then let me know.
No images because I'm lazy.

Equations of motion
v = u + at
v² = u² + 2as
s = ut + 0.5at²
s = 0.5(u+v)t

v is the final velocity
u is the initial velocity
a is the acceleration
s is distance between start and end points
t is time taken to reach a point on the path.

for other situations, distance = speed * time may be applied, i.e motion in a single plane.

Getting the distance between 2 points

This is very simple. It's a simple case of comparing co-ordinates.
Formula: √((X2 - X1)² + (Y2-Y1)²)
Where the 2 objects are A(X1,Y1) and B(X2,Y2)

Motion in a circle
The above formula can be used to find the radius of a circle.
With this value, you can then apply various things to it, for example, at any point on the circle, the distances to the centre will be
x:rcosθ
y:rsinθ

where r is the radius of the circle and θ is the angle that the line makes with the horizontal ((Y2-Y1)/(X2-X1))

Momentum

Momentum is useful for situations where you want to create a realistic engine, with each object having a mass.

p = mv
p is momentum
m is mass
v is velocity.

Conservation of momentum

If you have 2 objects that collide, momentum is conserved.
This explains how to deal with that if the collision is head on (i.e both objects are moving in the same plane)

If the objects stay as seperate particles:
m1u1 + m2u2 = m1v1 + m2v2

where particles of mass m1 and m2 have initial speed of u1 and u2 and final velocities of v1 and v2 respectively.
If an object is moving in the opposite direction to the other, it's velocity will be -u or -v, relative to the first object.
Therefore consider it with the direction of motion of 1 object.

If the objects coalesce (join together):
m1u1 + m2u2 = v(m1+m2)

Same as above, but there is only one final velocity.

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There are probably others.

If I can think of some, or people offer suggestions as to what they'd like to know, I'll make a part 2 or something.