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Homework Statement
I have a block of mass m on a horizontal surface, which is covered in oil. The tell me the viscous resistance force is a function of the velocity, F(v)=-cv1/2, where I am assuming c is a constant of some kind. I need to find the time that it will take for the block to stop. The initial velocity is V0 at x=0
Homework Equations
Equations of motion
Newton's laws
The Attempt at a Solution
I thought that I could use ΣF=ma. Then in my equations of motion solve for a=(V-V0)/t
Since the vertical forces cancel out, the equation would then be:
-cv1/2=m((V-V0)/t)
The problem is if I want the block to stop then V will be 0 and my equation doesn't work. Since the resistance is a function of V will I have to integrate it ?