...
........◄◄◄..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
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or E = m
v
/√(1 – v
/ c
)
so ..........
time to hit the sack..... ZZzzzz