Physics Time Dilation?

Question

Im dealing with this question..

What speed would a clock have to be moving so time dilation would cause it to run slower by 50%?

Im kind of confused on how to take the approach to this question, Im not sure how to take the speeds of them. Any help of this would be greatly appreciated.

Answer 1

TJ said:

"As you approach the speed of light, time slows down."

True.

"At c/2, it would run 50% slower."

Not true. The equation is not linear. Bob, use this formula:

("slow" clock rate) / ("regular" clock rate) = sqrt(1 - v^2/c^2)

In your case, the ratio of the clock rates is 50% (i.e. 1/2). So:

1/2 = sqrt(1 - v^2/c^2)

Now just solve for v. (BTW, the answer is not 99% of c, in spite of what katz149 says. He needs to get a new spreadsheet!)

Answer 2

The fundamental equation is the Lorentz's Transformation for the time interval:

t'=(gamma)t where t' is the time on the moving reference frame, t is the time measured in the rest frame and gamma=(1-(v/c)^2)^-1/2 so
when the the condition you have means that t'/2=t this is how it works:

you want the moving clock to run slower tha the resting clock by 50% this means that a time interval in the moving frame is twice the size of a time interval in the resting one, that is to say weareas the in tho moving clock has passed one second in the rest frame the clock has elapsed 2 seconds.

so we introduce this condition the equation above and :

t'=(gamma)t'/2 and after canceling the t's (we can d this since the time interval cannot be zero) we obtain:

gamma=2 then (1-(v/c)^2)^-1/2=2 so (1-(v/c)^2)^1/2=1/2

therefor 1-(v/c)^2=1/4 wich means that v^2=(3/4)c^2

so finally v=((3/4)^1/2)c

and aproximately v=0.8660c

Answer 3

There is a parameter called gamma that describes the amount of time dilation, Lorenz contraction, and other effects of special relativity.

If c is the speed of light in a vacuum and v is the velocity of the moving object, gamma - its closest ASCII lookalike is y, but if the coding on your machine is right, the real gamma looks like this in this particular typeface: γ - is given by

y = 1 / sqrt ( 1 - (v/c)^2 )

A graph of 1 / y on the vertical axis and v/c on the horizontal axis looks like a quarter circle.

If a clock on a rocket moving past you at v/c, the clock will seem to be running at a rate of 1/y times what it would at rest.

In your example, 1 / y = 0.5, so the clock must be moving at a speed of sqrt (3) / 2 or 0.866 times the speed of light.

Answer 4

As you approach the speed of light, time slows down. At c/2, it would run 50% slower.

Answer 5

if 2 ppl are at the same place at exactly same time. lets suppose time to be 2 am.

If person A goes at the speed of 2c (whr c is speed of light) for half hr. If he then returns ie time is 2:30am according to person A. But according to person B time would be 3 am.

So it is what time dilation is all about.

I hope it helped!

Answer 6

Lifetime measured on this planet = (two.6x10^-eight) / sqrt(a million-v^two/c^two) = a million.three x 10^-nine Distance = vt = zero.ninety eight * 3x10^eight *a million.three x 10^-7 = forty eight.two kilo meters w/o time dilation: distance = zero.ninety eight * three x 10^eight * two.6 x 10^-eight = nine.6 kilo meters that different man used to be rather flawed you didnt percentage the solutions together with your peers did you................... good with a view to lend you a hand i might have got to reduce off my possess jk however with a view to do that you ought to play a speedy sport of spoons even as within the physics lab if educate fundamental isn't there nathan rattling nathan first-rate considering although, asking yahoo solutions to support us out

Answer 7

the answer. according to microsoft excel is .99 the speed of light. Dialation occurs on a curve not a line.