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Find initial velocity of the spaceship

  1. Mar 8, 2005 #1
    a) The acceleration of a space ship is given by a(t) = 3 m/s2 – (2 m/s3 ) t. Find the initial velocity V0 so that the space ship is at the same point where it started after 5 seconds.

    No idea how to do this one, but do you need to integrate?

    Ty
     
  2. jcsd
  3. Mar 8, 2005 #2
    Yes you will have to integrate.
     
  4. Mar 8, 2005 #3
    How do you integrate that?
     
  5. Mar 8, 2005 #4

    xanthym

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    a(t) = (dv/dt) = 3 - 2t ::: ⇒ v(t) = ∫ (3 - 2t) dt = 3t - t2 + v0
    v(t) = (dz/dt) = 3t - t2 + v0 ::: ⇒ z(t) = ∫ (3t - t2 + v0) dt = 3t2/2 - t3/3 + v0t + z0

    Problem requires that {z(5) = z0}, so that:
    z(5) = z0 = 3(5)2/2 - (5)3/3 + v0(5) + z0
    ⇒ 0 = (37.5) - (41.7) + 5v0
    ⇒ 5v0 = 4.2
    v0 = (0.84 m/sec)


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