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6 March, 11:54

A soccer player kicks a ball, giving it an initial velocity of 9.0 m/s in the positive x - direction. Because of the wet grass and dirt, the ball slows uniformly to 3.00 m/s when it has travelled 30.0 m. Determine the ball's acceleration? Hint: Acceleration is a vector and direction must be specified (SLO 1)

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  1. 6 March, 12:19
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    a = - 1.2 m/s²

    Direction of a : in the negative x - direction

    Explanation:

    Because the ball moves with uniformly accelerated movement we apply the following formula:

    vf²=v₀²+2*a*d Formula (1)

    Where:

    d:displacement in meters (m)

    v₀: initial velocity in m/s

    vf: final velocity in m/s

    a: acceleration in m/s²

    Known data

    v₀ = 9.0 m/s

    vf = 3.00 m/s

    d = 30.0 m.

    Problem development

    We replace data in the formula (1) to calculate acceleration:

    vf²=v₀²+2*a*d

    (3) ² = (9) ² + (2 * 30) * a

    9=81 + (60) * a

    9-81 = (60) * a

    -72 = (60) * a

    a = - 72/60

    a = - 1.2 m/s²

    Direction of a : in the negative x - direction
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