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23 July, 13:15

ll of mass m is thrown vertically upward with an initial speed of v0. It experiences a force of air resistance given by F = - kv, where k is a positive constant. The positive direction for all vector quantities is upward. The differential equation for determining the instantaneous speed v of the ball in terms of time t as the ball moves upward is

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  1. 23 July, 15:41
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    the diferencial equation is

    dv (t) / dt + (k/m) v (t) + g = 0

    Explanation:

    the differential equation for determining the instantaneous speed can be found from Newton's second law:

    F = m*a

    F drag + F gravity = m*a

    (-k*v) + (-m*g) = m*a, where g is acceleration due to gravitational force

    since a = dv/dt and dividing both sides by m

    dv (t) / dt = - g - k/m v (t)

    or

    dv (t) / dt + (k/m) v (t) + g = 0
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