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Calculate tangential acceleration knowing velocity and time...

  1. Nov 2, 2015 #1
    1. The problem statement, all variables and given/known data

    A train moves along a circle with radius R = 2 km. The train accelerates with a constant rate, from v1 = 30 km/h to v2 = 100 km/h. It crosses SF = 1200 m during the acceleration.
    a) Find the time tF of the acceleration.
    b) What is the tangential acceleration aT of the train?

    2. Relevant equations

    aT = Δv/Δt
    and anything relevant to non-constant displacement along a circle.

    3. The attempt at a solution

    Although it seems pretty easy, I am unsure on how to use the formulas I have. For the first question, I calculated the average speed during the acceleration ((100-30)/2 + 30 = 65 km/h) and then the time it takes at this speed to cross 1.2 km (1 min 6s).

    Then I have a lot of different formulas for how to calculate the tangential acceleration, especially that one:
    aT = Δv/Δt

    Can someone please help me with how to use this formula in a problem? I would guess Δd is (100 - 30)⋅602 (in order to get a result in m/s) and Δt is 66s, am I right?

    Thank you very much in advance for your answers.


    J.
     
  2. jcsd
  3. Nov 2, 2015 #2

    mfb

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    During the acceleration? While it is still accelerating?

    Why do you need a Δd here (and why should it be different from 1200m?), and where do the factors of 60 come from?
     
  4. Nov 3, 2015 #3
    Yes it is still accelerating for 1200m. The factors of 60 are for the velocity to be expressed in m/s, I meant Δv and not Δd of course.
     
  5. Nov 3, 2015 #4
    That gives me a tangential acceleration of 3818.2 m/s2 btw.
     
  6. Nov 3, 2015 #5

    SammyS

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    That will give km/s, not m/s.
     
  7. Nov 3, 2015 #6

    mfb

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    It should give km/(3600h).

    That would be lethal.
     
  8. Nov 3, 2015 #7

    SammyS

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    Yes, of course!

    I stand corrected. DUH!
     
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