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Math Help - Velocity and Acceleration for a Trig equation

  1. #1
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    Velocity and Acceleration for a Trig equation

    A particle moves in a straight line along the x-axis so that its position, x(t), at time t seconds, t≥0, is given by x=sin(pi.t^2)

    a) Find expressions for the velocity and acceleration of the particle at time t

    b) Find the times for which the particle is stationary

    If anyone could help with this question, that would be great
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Velocity and Acceleration for a Trig equation

    Do you know the definitions of velocity and acceleration?
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  3. #3
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    Re: Velocity and Acceleration for a Trig equation

    I think velocity will just be the derivative, however I have forgotten what acceleration will be
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    Re: Velocity and Acceleration for a Trig equation

    Quote Originally Posted by gbooker View Post
    I think velocity will just be the derivative, however I have forgotten what acceleration will be
    Acceleration is the second derivative of displacement (or the first derivative of velocity)
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  5. #5
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    Re: Velocity and Acceleration for a Trig equation

    ok so as a result of that the derivative (velocity) = (cos.pi.x^2). (2x.pi)

    so does that mean for part b is it just solve for when velocity=0?
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  6. #6
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    Re: Velocity and Acceleration for a Trig equation

    Quote Originally Posted by gbooker View Post
    ok so as a result of that the derivative (velocity) = (cos.pi.x^2). (2x.pi)

    so does that mean for part b is it just solve for when velocity=0?
    yes, v(t) = 2\pi t \cdot \cos(\pi t^2) = 0

    solve for those values of t \ge 0 that make the velocity zero.
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