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Example of x0 in the kinematic equation for displacement

  1. May 2, 2013 #1
    In the kinematic equation x = x0 + v0 * t + .5 * a * t^2, can someone give me an example in which x0 has a value that is not zero?
     
  2. jcsd
  3. May 2, 2013 #2

    WannabeNewton

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    Hi e-zero! ##x_{0}## is just the initial position of the test particle that you are looking at the trajectory of under constant acceleration; similarly ##v_{0}## is just the initial velocity of the trajectory. You can choose them to be whatever you want them to be. I can for example drop my object from a height of 5 meters from the ground, starting at rest, in which case ##x_{0} = 5 \text{m}## , ##v_{0} = 0 \text{m /s}## , and (ignoring air resistance) the equations of motion become ##x(t) = 5 \text{m} - \frac{1}{2}gt^{2}##. Hope that helps friend!
     
  4. May 2, 2013 #3
    Ok, is there an example where both x and x0 are both not zero?
     
  5. May 2, 2013 #4

    WannabeNewton

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    ##x(t)## is a function of time so it will change its value at every instant of time. In the example I gave above, ##x(t)## is the height of the particle from the ground so it will be non-zero up until the first time the particle hits the ground.
     
  6. May 2, 2013 #5
    Can you give an example that does not involve vertical, but horizontal motion in which x and x0 are both not zero?
     
  7. May 2, 2013 #6

    WannabeNewton

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    Sure! Choose an origin and take a particle located 5 meters horizontally from that origin and give it an initial kick of 5 meters per second in the horizontal direction.
     
  8. May 2, 2013 #7
    Ok. I was just confusing myself. It all depends on the question if you should take x0 to be zero or not.
     
  9. May 2, 2013 #8

    WannabeNewton

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    Indeed! Good luck with your studies friend :)
     
  10. May 2, 2013 #9
    Thanks
     
  11. May 2, 2013 #10

    fluidistic

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    Not really. It depends on where you want the origin of your system of coordinates to be. In WBN's example, he chose the ground as origin. That's why x_0 in his case was 5m. For the same example he could have chosen its origin 5 meters above the ground, in which case x_0 would have been 0.
     
  12. May 2, 2013 #11
    Ok, I see.
     
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