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Thread: Maximum acceleration from velocity equation?

  1. #1
    Junior Member
    Join Date
    May 2006
    Posts
    67

    Maximum acceleration from velocity equation?

    Hey guise,

    I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is

    a(t) = Cos(Pi/30t)

    the velocity is v(t) = 30Sin(Pi/30t) + C

    and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct

    So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which equation do I solve? I realize this is conceptual in some ways.

    Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?

  2. #2
    Elite Member
    Join Date
    Jun 2007
    Posts
    12,834

    Re: Maximum acceleration from velocity equation?

    Quote Originally Posted by Jaskaran
    Hey guise,

    I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is

    a(t) = Cos(Pi/30t)

    the velocity is v(t) = 30Sin(Pi/30t) + C

    and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct

    So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which equation do I solve? I realize this is conceptual in some ways.

    Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?
    What is the condition for local "maximum/minimum" of a function?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Junior Member
    Join Date
    May 2006
    Posts
    67

    Re: Maximum acceleration from velocity equation?

    Quote Originally Posted by Subhotosh Khan
    Quote Originally Posted by Jaskaran
    Hey guise,

    I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is

    a(t) = Cos(Pi/30t)

    the velocity is v(t) = 30Sin(Pi/30t) + C

    and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct

    So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which equation do I solve? I realize this is conceptual in some ways.

    Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?
    What is the condition for local "maximum/minimum" of a function?
    You set acceleration = 0 and figure values, and figure out whether values before or after than are positive or negative.

  4. #4
    Elite Member
    Join Date
    Jun 2007
    Posts
    12,834

    Re: Maximum acceleration from velocity equation?

    Quote Originally Posted by Jaskaran
    Quote Originally Posted by Subhotosh Khan
    Quote Originally Posted by Jaskaran
    So given this, how do I find the max acceleration?
    What is the condition for local "maximum/minimum" of a function?
    You set acceleration = 0 and figure values, and figure out whether values before or after than are positive or negative.
    Local maximum/minimum of a function f(x) is at points where the derivative of the function is equal to zero (df/dx = 0)
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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