# Homework Help: Problem with Friction dependent on velocity, mostly a math problem.

1. Jan 28, 2012

### Simen

Hello, first time here for me, I hope I posted in the right subforum.
I have a task at hand, just started a new physics course, but sadly I am far from deft with mathematics, and my physics book is in a different language and uses different notation than I am used to. The part I am having trouble with is the following:

1. The problem statement, all variables and given/known data

We have a block, with the starting velocity 5m/s.
The friction from the block is given as a = -μ|v|g
Where μ = 0.1 and g = 9.8 m/s^2

Find v(t)

2. Relevant equations
v(t) = v(0)+at

a = dv/dt = (d/dt)(dx/dt) =(d2x)/dt2

3. The attempt at a solution

As it stands now, I I realize I should integrate a in order to obtain v(t), but I am horrible at math, and do not know where to start, for some reason I keep ending up with an expression without v at all, but that does not help things either. If someone could show me the first steps in this that would be great. I've written a python program to solve it numerically as well, though I can not check if it is working, because I am too inept to get my analytical solution.

Would something like this be a step in the right direction?
a = -0.98|v|
v(0) = 5 m/s
a(0) = 0

dv/dt = -0.98*v

dv/dt2 = -0.98*v*dt

(dv/dt2)1/v = -0.98dt

And then integrate from here? Could someone show me an example? Doesn't need to have any of my numbers, so long as I can learn some of what I need from it.

If anyone could provide any help, that would be greatly appreciated!

2. Jan 28, 2012

### tiny-tim

Welcome to PF!

Hello Simen! Welcome to PF!
(you left out a µ)

Now you "separate the variables" …

dv/v = -0.98µdt …

carry on from there

3. Jan 29, 2012

### Simen

Thanks for the welcome:)

I actually didn't forget the μ, since μ = 0.1 and it was to be multiplied with g = 9.8 I just multiplied them before I started integrating.

Anyways, does this look right?
dv/dt = -0.98v

dv/v = -0.98dt

Integrate:

ln(v)-ln(v0)=-0.98(t-t0)

Clean up a little:
v/v0=e-0.98(t-t0)

v = v0e-0.98(t-t0)

Then putting in t0 = 0 and v0 = 5 and getting
v(t) = 5e-0.98t