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Math Help - Velocity

  1. #1
    JC1341
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    Velocity

    " An object moves along the x-axis with initial position x(0) = 2

    The velocity of the object at time t>/= 0 is given by v(t) = sin(pi/3t)

    A: for 3< t < 4.5 the velocity of the object is decreasing
    B: for 3< t < 4.5 the speed of the object is increasing

    Are either both of these statements correct? For each statement provide a reason why it is correct or not.


    What is the position of the object at time t=4? "


    help please, thanks
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  2. #2
    Senior Member JaneBennet's Avatar
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    Differentiate v(t) with respect to t to find the acceleration, a(t). The velocity is decreasing if a(t) < 0 and increasing if a(t) > 0. The speed is increasing if either v(t) > 0 and a(t) > 0, or v(t) < 0 and a(t) < 0; it is decreasing if v(t) and a(t) have opposite signs.

    To find the position, you need to integrate v(t) with respect to t.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by JC1341 View Post
    " An object moves along the x-axis with initial position x(0) = 2

    The velocity of the object at time t>/= 0 is given by v(t) = sin(pi/3t)
    Please be more carefull with your notation. Do you mean:

    v(t)=sin( (pi/3) t )

    or

    v(t)=sin( pi/(3t) )

    The first seems more likely, but don't make us guess.

    (if you don't want to differentiate whatever you do mean, you could
    try sketching the velocity time curve)

    RonL
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