Ft 32 Lights
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Hypothetically if you could accelerate a rocket to the speed of light how long would it take at 32 ft/sec/sec?
If you use the pre-Einsteinian (i.e. WRONG) rules of acceleration, the time to reach a speed "v" while accelerating at 1 g, is given by:
t = v/g
Plug in "c" (speed of light) for v, and you get:
t = c/g = (3×10^8m/s) / (9.8m/s²)
= 30.6 million seconds, or about 354 days.
However, Einstein showed that the above formula is only an approximation, and really only works well when the speed v is small compared to "c". The more accurate formula is:
t = (v/g) / sqrt(1-(v/c)²)
Unfortunately, you can see that if you try plugging in v = c into that equation, the time "t" becomes infinite. That's another way of saying that you CANNOT ever really reach speed "c" by accelerating at 1 g (or at any other acceleration for that matter).
This is an expression of the fact that space and time are intimately tied together by the universal constant "c" (that constant appears in many of the (corrected) equations relating space, time, matter and energy). One of the consequences of that connection is that spacetime prevents material objects from reaching speed "c".
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May 1, 2011 by 
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