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26 November, 17:19

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 / ms2. If the acceleration of the object becomes 6 / ms2, what is the force

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  1. 26 November, 18:18
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    The force is 12 N

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - Direct variation is a relationship between two variables that can

    be expressed by an equation in which one variable is equal to a

    constant times the other

    - If y ∝ x, then y = kx, where k is the constant of variation

    * Lets solve the problem

    - The force acting on the object varies directly with the object's

    acceleration

    ∵ The force is F in newtons and a is the acceleration is m/s²

    ∴ F ∝ a

    ∴ F = ka

    - To find k substitute F and a by the initial values of them

    ∵ A force of 10 N acts on a certain object, the acceleration of the

    object is 5 m/s²

    ∵ F = 10 N when a = 5 m/s²

    ∵ F = ka

    ∴ 10 = k (5)

    - Divide both sides by 5

    ∴ K = 2

    - Substitute the value of k in the equation

    ∴ F = 2a

    - Lets find the force when the acceleration is 6 m/s²

    ∵ a = 6 m/s²

    ∴ F = 2 (6) = 12

    * The force is 12 N
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