Question

About time and velocity of the light (quick question)

Answer 1

So I know that
T'=\[\frac{ T }{ \sqrt{1-(\frac{ V }{ C })^{2}} } \]

At what velocity is my time doubled?

Answer 2

For T' to double, you'll need T to be divided by 0.5 (since dividing by half is the same as multiplying by 2).

So the denominator will need to equal 0.5... so set the denominator equal to 0.5 and solve for v.

Answer 3

\[\Large \sqrt{1-(\frac{ V }{ C })^{2}} = 0.5\]
start by squaring both sides

Answer 4

\[0.25=1-(\frac{ V }{ C })^{2}\]
So \[V=\frac{ \sqrt{0.75} }{ C }\]

Answer 5

I thought it was half the velocity of the light

Answer 6

Your rearrangement doesn't look right \[0.75=(\frac{ V }{ C })^{2}\]\[\sqrt {0.75} = \frac{ v }{ c }\]now multiply both sides by c

Answer 7

Ok, are you sure this is the answer. Someone told me it was 0.5C

Answer 8

And if they give me another time, what should I do?

Answer 9

\[\Large v = c \sqrt{0.75}\] you could plug in 0.5c to check it doesnt double... \[\Large T' = \frac{ T }{ \sqrt { 1- \left( \frac{ 0.5c }{c } \right)^2 } }\]which is \[\Large T' = \frac{ T }{ \sqrt { 1- 0.25 } } = \frac{ T }{ \sqrt {0.75 } }\]which is nothing like doubling.

Answer 10

Ok, you are right

Answer 11

So what should I do if they ask for another time?

Answer 12

Let's say, 3

Answer 13

If the time triples, that's the same as dividing T by 1/3. So you'd set the denom equal to 1/3

Answer 14

If time quadrupled, what would the denominator be equal to?

Answer 15

1/4

Answer 16

So for 3 the velocity would be \[\sqrt{0.7}C\]

Answer 17

But here you are multiplying T, not T'

Answer 18

Well if you multiply T by 2, what happens to T'?

Answer 19

Stupid question, sorry haha

Answer 20

haha no prob. It's not always immediately obvious.