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MrPyromaniac
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Homework Statement
A block of mass m, which has an initial velocity v0 at time t = 0, slides on a horizontal surface. If the sliding friction force f exerted on the block by the surface is directly proportional to its velocity (that is, f = -kv),
A) Write a differential equation for the velocity v in terms of the given variables and fundamental constants.
B) Find the acceleration a of the block in terms of m, k, and v.
C) The speed v of the block as a function of time t.
D) The total distance the block slides.
Homework Equations
F = m*a
The Attempt at a Solution
I understand why B is a = (-kv)/m, and I know the answer to a is dv/dt = -kv/m but I don't know why, and I have no idea how to solve for velocity. Assuming I get a function for the velocity, what general equation would I use to solve for the total distance? I originally thought x-x0 = v0*t + (1/2)*a*t^2, but the acceleration isn't uniform.