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27 June, 02:02

At t = 0 the components of a radio-controlled car's velocity are vx = 0.5 m/s and vy = 1.2 m/s. Find the components of the car's velocity at t = 4.1 s, given that the components of its average acceleration during this period are ax = 2 m/s2 and ay = - 1 m/s2.

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  1. 27 June, 02:56
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    vx' = 8.7 m/s

    vy' = - 2.9 m/s

    Explanation:

    The average acceleration during a time period is given by the formula:

    a = (v' - v) / (t' - t)

    where,

    a = average acceleration

    v' = Final Velocity

    v = Initial Velocity

    t' = Ending Time

    t = Starting Time

    Now, for x-component of velocity:

    a = ax = 2 m/s²

    v' = vx' = ?

    v = vx = 0.5 m/s

    t' = 4.1 s

    t = 0 s

    Therefore,

    2 m/s² = (vx' - 0.5 m/s) / (4.1s - 0s)

    (2 m/s²) (4.1 s) = vx' - 0.5 m/s

    8.2 m/s + 0.5 m/s = vx'

    vx' = 8.7 m/s

    For y - component of velocity:

    a = ay = - 1 m/s²

    v' = vy' = ?

    v = vy = 1.2 m/s

    t' = 4.1 s

    t = 0 s

    Therefore,

    - 1 m/s² = (vy' - 1.2 m/s) / (4.1s - 0s)

    ( - 1 m/s²) (4.1 s) = vy' - 1.2 m/s

    - 4.1 m/s + 1.2 m/s = vy'

    vy' = - 2.9 m/s
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