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Acceleration, velocity, distance, speed and time help please

  1. Mar 12, 2007 #1
    Hi Everyone,
    This might be a little too complex for me to understand the answer, But here goes:

    1) I have a fictional spacecraft, frictonless and an infinite supply of fuel.

    2) It is able to accelerate at 9.8 m/s/s.

    3) I want to travel between 2 planets 100 million kilometers apart.

    4) I want to accelerate 1/2 way then deccelerate the rest of the way.

    I know:

    distance = 100,000,000km = 100,000,000,000m
    acceleration = 9.8m/s/s
    time = ? in seconds
    velocity = 9.8*time = ?m/s

    I can break the trip in two 50,000,000,000m if I figure the time and max velocity for the acceleration phase, I know it for the deceleration phase.

    if I remember right (high school physics was 30 years ago) I would travel
    4.9m, ending with a velocity of 9.8m/s after the first second.
    9.8m, (total 14.7m), ending with a velocity of 19.6m/s after the second second.
    19.6m, (total 34.3m), ending with a velocity of 29.4m/s after the third second.

    I know I could use a spread sheet and just keep doubling the distance, adding it to the total distance and add another 9.8m/s to the velocity until I got to 50,000,000,000m, But there must be a formula to figure this out, my question is where can I find the formula.
  2. jcsd
  3. Mar 12, 2007 #2


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  4. Mar 12, 2007 #3


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    This calculation would require the use of special relativity. Do you kno wsome special relativity? (if you use the non-relativistic kinematic equations with an acceleration of 9.8 m/s^2, you will end up having a spacecraft moving faster than the speed of light, which is unphysical).
  5. Mar 12, 2007 #4


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    Yeah I guess it does. I didn't look at the numbers that closely. You can find relativistic equations of motion in the same thread I posted earlier I think.
  6. Mar 12, 2007 #5
    Space to work out this problem.

    I'll try to work this out, It might take a while though. :smile:

    Things I know:
    c = 299,792,458m/s
    c^2 = 89,875,517,873,681,800m/s
    a = 9.8m/s/s

    Things I might have to work out:

    [tex]\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}[/tex]

    My Brain Hurts, this as far as I go tonight, I'll try again tomorrow.
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