Example 1: The downward velocity v of a falling object with mass m and air resistance coefficient satisfies
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An object of mass m is given an initial downward velocity and allowed to fall under the influence of gravity. Assume that the gravitational force is constant and the force due to air resistance is proportional to the velocity of the object. Then the equation of motion for this object with respect to velocity will be differential equation of type
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17. A falling object experiences a force due to air resistance that is proportional to its velocity. This can be modelled by the differential equation m dv/dt = mg - kv where kv is the force due to air resistance and k is a constant. Solve the differential equation to obtain an expression for the velocity v of a falling object, assuming that the object falls from rest when t = 0. Note: Leave m, g and k as unknown constants in your expression.
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'(a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity; with a constant of proportionality k > 0 (this is called the drag coefficient) . Take the downward direction to be positive. Solve the differential equation subject to the initial condition v(t = 0) = vo. Determine the terminal velocity of the mass.'
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