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Math Help - Finding when the velocity equals x.

  1. #1
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    Finding when the velocity equals x.

    Hey! I know I've had a lot of questions on here over the past couple days, but I am just ensuring I understand what I am doing, and you guys do such a great job of explaining everything!
    Okay, I have a derivative question that I am not entirely sure how to solve, so I was hoping you guys could help me out!

    Question
    The position function of an object moving along a straight line is given by the function s(t) = t^3 - 15t^2 + 48t - 10 , where s is in metres and t s in seconds and  0<t<15 .
    i) When is the velocity the object greater than 21 m/s?
    ii) When is the speed of the object less than 21 m/s?

    Question
    I really have no idea how to solve for this! With the equation given I know the distance in metres after t seconds, but not the velocity, and the question is asking for velocity.
    How would I go about solving this question?
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  2. #2
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    Quote Originally Posted by Kakariki View Post

    i) When is the velocity the object greater than 21 m/s?
    Find s'(t)>21

    Quote Originally Posted by Kakariki View Post

    ii) When is the speed of the object less than 21 m/s?
    Do you mean \frac{m}{s^2} ?

    This needs to be confirmed.

    I think you are after s''(t)<21
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  3. #3
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    @pickslides
    Speed is the rate of change of distance with time.
    Velocity is the rate of change of displacement with time.

    which means:

    Speed is the first derivative of distance with respect to time.
    Velocity is the first derivative of displacement with respect to time.

    Let me clarify.

    v(t)=s'(t), that is the instantaneous velocity at time t.

    Velocity is speed with direction, and speed is velocity with no direction, so the speed equals |v(t)| or |s'(t)|.

    What she needs to find is:

    i) s'(t)>21

    ii)|s'(t)|<21
    Last edited by p0oint; June 8th 2010 at 04:14 AM.
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