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Evaluate a particles position

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data

    The position of a particle moving along the x axis varies in time according to the expression x = 3t 2, where x is in meters and t is in seconds. Evaluate its position at the following times.
    (
    a) t = 2.30 s


    (b) t = 2.30 s + Δt


    (c) Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 2.30 s.
    m/s


    2. Relevant equations

    Listed above.

    3. The attempt at a solution

    Well for part 'a)', I plugged in the given time (2.30) and got 15.87 meters.

    At part 'b)' is where I get stumped. What would you do to find delta t?

    Thanks.
     
  2. jcsd
  3. Sep 9, 2012 #2

    gneill

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    Staff: Mentor

    You don't find Δt; You plug in the symbol Δt and expand the expression; at this point it is simply a variable. It may be worthwhile to replace the initial value of t (2.30s) with a symbol, too. Say, to = 2.30s. This may help keep the subsequent manipulations neat.

    For part (c) you need to understand what is meant by Δx. That is, the change in x.
     
  4. Sep 9, 2012 #3
    Okay, so all you do is plug in the variables.

    So I came up with X = 3(T+TΔ)^2

    Would I FOIL it out, or something? How do I come up with a numerical answer?
     
  5. Sep 9, 2012 #4
    I just foiled and got 3(5.29 + 4.60ΔT + ΔT^2)

    Stuck here now, shoot. I have a feeling i'm way off....
     
  6. Sep 9, 2012 #5

    gneill

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    Staff: Mentor

    You don't. There's no numerical answer to this part unless a specific Δt is provided. A symbolic result is sometimes what you're looking for. Move on to the next part.
     
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