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Cryptologica
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Homework Statement
For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet = −mkv2, where k is a constant. The speed of the object after t = 0 is given by
v = vi/(1 + kvit).
(a) Find the position x of the object as a function of time. (Use the following as necessary: k, m, t, and vi.)
(b) Find the object's velocity as a function of position. (Use the following as necessary: k, m, t, vi, and x.)
Homework Equations
a = Δv/Δt
v = Δx/Δt
The Attempt at a Solution
I am suspecting that I need to integrate the given function to find the position function? I know that v = Δx/Δt, so we should have:
dx/dt = vi/(1 + kvit)
then we need to take the definite integral from x0 to xf or just 0 to xf. My calculus is a bit rough, but isn't this some sort of a separable differential equation? So we need to make all the x's and t's all on one side? Right now that seems, well, impossible since we have no x's? So do I need to find something involving v and x, then relate/substitute so I only have x's and t's? Help please...