...

..........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:

ct -. vt = .ct'

separate out t :

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

To get t on its own, divide both sides by (c -. v):

t.= ct' / (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