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5 October, 17:24

The position of a particle is given by the position vector, r (t) = (3t) i + (-4.9t2) j, where r is in meters and t is in seconds. a) What is its position at t = 2 s? b) What is the instantaneous velocity of the particle? c) What is the instantaneous velocity at t = 2 s? d) What is the acceleration of the particle? e) Sketch the position, velocity, and acceleration vectors at t = 2 s.

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  1. 5 October, 18:13
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    a)

    r (t) = (3t) i + (-4.9t2) j

    At t = 2

    r (t) = (3 x 2) i + (-4.9 x 2²) j

    = 6i - 19.6 j

    magnitude = R

    R² = 6² + 19.6²

    R = 20.5 m/s

    b)

    r (t) = (3t) i + (-4.9t2) j

    velocity

    = dr/dt = 3 i - 9.8 t j

    c)

    At t = 2

    instantaneous velocity

    = 3 i - 9.8 t j

    at t = 2

    = 3i - 9,8 x 2j

    = 3i - 19.6 j

    magnitude

    = 19.82 m/s

    d)

    acceleration a

    dr/dt = 3 i - 9.8 t j

    Again differentiating

    d²r/dt² = - 9.8 j

    acceleration = 9.8 m / s² towards - ve y axis.
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