# Dynamics help - Motion

1. Jan 27, 2009

### vdfortd

1. The problem statement, all variables and given/known data
An engineer designing a system to control router for a machining process models the system so that the router's acceleration (in in/s2) during an interval of time is given by a= -0.4v, where v is the velocity of the router in in/s2. When t=0, the position is s=0 and the velocity is v= 2 in/s. What is the position at t=3 seconds?

2. Relevant equations

a= dv/dt

3. The attempt at a solution

This section has to do with straight line motion when the acceleration depends on velocity or position.

This is what I tried to do:

a= -0.4v
a= dv/dt

dv/dt = -0.4v

dv/v= -0.4 dt

I integrated both sides and I got:

ln v = -.4t + C ( C = constant)

From my differential equations math class, we did problems like these and we got rid of the ln by making it all a power of e.

eln v = e -.4t + C

you get v= e-.4t+C or v= e-.4tC

Now I know this is wrong because we know that when t=0 v=2. Am I on the right track or did i do this completely wrong? Thanks for any help.

2. Jan 28, 2009

### nvn

vdfortd: Nice work. You are doing well, so far. You said, "Now I know this is wrong." That is not true. Go ahead and substitute t = 0 and v = 2 into your last equation, and see what you get. Solve for C. Now continue solving the problem.