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6 July, 13:24

A 0.333 kg particle with an initial velocity of 1.89 m/s is accelerated by a constant force of 1.64 N over a distance of 0.281 m. Use the concept of energy to determine the final velocity of the particle. (It is useful to double-check your answer by also solving the problem using Newton's Laws and the kinematic equations.)

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  1. 6 July, 13:29
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    2.5 m/s

    Explanation:

    m = 0.333 kg

    u = 1.89 m/s

    F = 1.64 N

    S = 0.281 m

    Let the final velocity is v.

    By energy conservation

    Work done = Change in kinetic energy

    F x S = 1/2 m (v^2 - u^2)

    1.64 x 0.281 = 0.5 x 0.333 (v^2 - 1.89^2)

    2.767 = v^2 - 3.5721

    v^2 = 6.339

    v = 2.5 m/s

    By using kinematics

    Let a be the acceleration

    a = F / m = 1.64 / 0.333 = 4.925 m/s^2

    Use third equation of motion

    v^2 = u^2 + 2as

    v^2 = 1.89^2 + 2 x 4.925 x 0.281

    v^2 = 6.339

    v = 2.5 m/s
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