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Math Help - 2 Calculus questions... (particle motion and derivatives)

  1. #1
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    2 Calculus questions... (particle motion and derivatives)

    1) A particle moves along the x-axis so that, at any time t≥0, its acceleration is given by a(t)=6t-3. At time t=0, the velocity of the particle is -18, and its position is -27.
    a) Find v(t), the velocity of the particle at any time t≥0.
    b) For what values of t≥0 is the particle moving to the right?
    c) Find x(t), the position of the particle at any time t≥0.

    2) Let y=2e^(sinx)
    a) Calculate dy/dx (1st derivative) and d2y/dx2 (2nd derivative).
    b) If x and y both vary with time in such a way that y increased at a steady rate of 5 units per second, at what rate is x changing when x=pi?

    Any help would be appreciated, even if you just explain to me the steps or methods I should be using.
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  2. #2
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    Quote Originally Posted by macroecon View Post
    1) A particle moves along the x-axis so that, at any time t≥0, its acceleration is given by a(t)=6t-3. At time t=0, the velocity of the particle is -18, and its position is -27.
    a) Find v(t), the velocity of the particle at any time t≥0.
    b) For what values of t≥0 is the particle moving to the right?
    c) Find x(t), the position of the particle at any time t≥0.

    2) Let y=2e^(sinx)
    a) Calculate dy/dx (1st derivative) and d2y/dx2 (2nd derivative).
    b) If x and y both vary with time in such a way that y increased at a steady rate of 5 units per second, at what rate is x changing when x=pi?

    Any help would be appreciated, even if you just explain to me the steps or methods I should be using.
    for (a) i think you should integrate a(t).
    for (c) the same thing, integrate v(t).
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  3. #3
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    so for #1
    a) i ended up with v(t)=3t^2-3t-18 or 3(t-3)(t+2)
    b) t≥3
    c) x(t)=(t^3)-(3/2t^2)-18t-27

    Can anyone check that?
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  4. #4
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    Quote Originally Posted by macroecon View Post
    so for #1
    a) i ended up with v(t)=3t^2-3t-18 or 3(t-3)(t+2)
    b) t≥3
    c) x(t)=(t^3)-(3/2t^2)-18t-27

    Can anyone check that?
    I agree .
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