- #1

ggb123

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## Homework Statement

A rock with mass "m" slides with initial velocity on a horizontal surface. A retarding force F that the surface exerts on the rock is proportional to the square root of the instantaneous velocity of the rock: F = -k * v^(0.5)

Find the equation for velocity as a function of time.

## Homework Equations

F = ma

a = dv/dt

## The Attempt at a Solution

I'm using online software and used up all my attempts at the answer, so it gave it to me:

vi = initial velocity

v = vi - ((vi)^0.5 * k * t)/m + (k^2 * t^2)/(4m^2)

And I have no idea how to get this. I'm thinking this is because I don't know much about integration. I'm hoping somebody could help me out in explaining this to me, even just a brief outline of the steps to the final answer would be great.

Any help is really appreciated, thanks