Oh, and I forgot to mention, the final velocity is twice the average velocity in the special case that the object starts from rest and accelerates at constant velocity. If these conditions are met, then the final velocity is vf=a*T, the total distance is (1/2)a*T\stackrel{2}{}, and the average...
First of all, the final velocity is not generally the average velocity times 2. Imagine that the your object were to go from zero to 1 m/s really quickly, and then traveled at 1 m/s for the rest of the trip (if you think this is unrealistic, think of a scrap of paper dropped in the air- it gets...
The key formula here will be the binomial distribution. It allows you to calculate the probability that you will obtain a specified result a specified number of times, given the number of total trials, and provided that there are only two possible outcomes. The formula is...
This theorem can't be proved, because (as noted by LCKurtz) it is simply false. A simple counter can be shown by letting A=B=C=i, D=j where i,j, and k are the unit vectors in the x,y, and z directions (respectively). Then
A x (B x (C x D))=i x (i x (i x j))
=i x (i x (k))
=i x (-j)
A x (B...