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..........BACK .(to time dilation)

Manipulation of formula is a dead cinch. Just a few simple rules that are obvious once you understand that the equals sign is like the pivot of a see-saw which must remain horizontal. Do what you like to either side, so long as you load (or unload) the other side likewise - that is ALL of the other side, not just a bit of it.

Some of those simple rules will appear as we move through the following process:

To make t the subject of the formula:

(ct/2) = (vt/2) + (ct'/2) First simplify by dividing both sides (that is the whole of both sides) by 1/2 :

(ct) = (vt) + (ct') Now get all the bits containing t on the same side, so subtract (vt) from both sides:

(ct) - .(vt) = . (ct') Get rid of brackets:

c t -. v t = .c t' separate out t :

t (c -. v ) . = .c t' To get t on its own, divide both sides by (c -. v ):

t .= c t' / (c -. v )

Simplify the right side of the formula by dividing ALL OF the top and bottom by c :

t .= t' / (1 -. v / c )

And finally squareroot both sides:

So t .t = t'/(1 – v / c )

THIS important formula was derived solely from the below diagram:

. Any aspect of a moving object can likewise be represented, giving rise to formula, for instance, that represents how the effective mass of an object is affected by being moved (m = rest mass) :

m = m /(1 – v / c )

Also F = m.a .... where F is force and a is acceleration

we've seen that velocity v = d/t ..so.. d = vt

but acceleration a = v/t = d/t and work W (or Energy E) = F.d = md /t = mv or E = m v /(1 – v / c )

so ..........

time to hit the sack..... ZZzzzz