Suppose a block sliding on a slippery horizontal surface experiences a drag force F=-cv3/2 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.
The Attempt at a Solution
I took the integral of the drag force
mdv = -cv3/2 dt
int [dv/v3/2]= -c/m * int[dt]
-2/v1/2 + 2/v01/2 = -c/m * t
Isolating for v:
v= [v01/2/ 1+ (cv01/2t/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.