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13 December, 13:47

The position vector for particle A is cos (t) i, and the position vector for particle B is sin (t) j. What is the difference in acceleration (i. e. the relative acceleration) between particle A and B at any time t? The acceleration vector of a particle moving in space is the second derivative of the position vector

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  1. 13 December, 16:38
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    sin (t) j - cos (t) i

    Step-by-step explanation:

    Let's start with A:

    Position vector = cos (t) i

    Velocity vector = - sin (t) i (differentiating the position vector)

    acceleration vector = - cos (t) i (differentiating the velocity vector)

    Then we go to B:

    Position vector = sin (t) j

    Velocity vector = cos (t) j

    acceleration vector = - sin (t) j

    Relative acceleration = - cos (t) i - (-sin (t) j) = sin (t) j - cos (t) i
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