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Math Help - Acceleration vector and speed

  1. #1
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    Unhappy Acceleration vector and speed

    Ap Calc exam tomorrow, and I really need to know how to do this...

    It is given that an object is moving along a curve in an xy-plane at position (x(t), y(t)), where dx/dt = arcsin(1-2(e^-t)) and dy/dt = (4t)/(1+(t^3)).
    At t=2, the object is at (6,3).

    The problem asks to find the acceleration vector and speed of object at t=2.

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  2. #2
    Junior Member piglet's Avatar
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    Quote Originally Posted by BeiW View Post
    Ap Calc exam tomorrow, and I really need to know how to do this...

    It is given that an object is moving along a curve in an xy-plane at position (x(t), y(t)), where dx/dt = arcsin(1-2(e^-t)) and dy/dt = (4t)/(1+(t^3)).
    At t=2, the object is at (6,3).

    The problem asks to find the acceleration vector and speed of object at t=2.

    Well acceleration is the first derivative of velocity and therefore it is the second position of position.

    So just differentiate \frac{dx}{dt} to get the acceleration in the x direction and differentiate  \frac{dy}{dt} to get the acceleration in the y direction.

    To find the speed at t=2, use the parametric differentiation formula  \frac{dy}{dx} =\frac {\frac{dy}{dt}}{\frac{dx}{dt}} and fill in t = 2
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