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## Homework Statement

Suppose a block sliding on a slippery horizontal surface experiences a drag force F=-cv

^{3/2 }where c is a positive constant. At time t=0, the block is at position x=0 with initial positive velocity. Find the velocity and position as a function of time. Derive an expression for the limiting distance the block travels, or show that there is no limit.

## Homework Equations

F=-cv

^{3/2}

## The Attempt at a Solution

*For velocity:*I took the integral of the drag force

mdv = -cv

^{3/2}dt

int [dv/v

^{3/2}]= -c/m * int[dt]

-2/v

^{1/2}+ 2/v

_{0}

^{1/2}= -c/m * t

*Isolating for v:*

v= [v

_{0}

^{1/2}/ 1+ (cv

_{0}

^{1/2}t/2m)]

^{2}

Can someone kindly check the arithmetic if I got it right.

As for position, I have trouble dealing with the integral of the velocity function. If someone can help me regarding this, it would be greatly appreciated.

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