# Force related to distance question

1. May 28, 2013

### joshmccraney

1. The problem statement, all variables and given/known data
So I have worked through most of the problem and what I have so far is correct. Basically, I have force as a function of time which, when exerted on an object, moves the object up a 15 degree slant. Given two points in times, my question reduces to finding the total distance traveled within this time period. It should be known I have initial and final velocities.

2. Relevant equations
work/energy seems useful here $U=\Delta V_G + \Delta T$

i don't think i need impulse, or namely $\int \sum F dt= \Delta G$ as this deals explicitly with time, which I have already used to get the force function (though I could be wrong)

3. The attempt at a solution
I was thinking $U=\int F ds = m g sin(15) s + m {{V_2}^2}/2 - m {{V_1}^2}/2$ where $s$ is the distance travelled I am looking for and the force function $F$ is changed to only account for forces other than gravity (since the $\Delta V_G$ term accounts for potential gravity.

but then, since $F$ is a function of time, i'm not sure how to proceed (if you need the force function I can give it, but it's kind of long)

I know both initial and final velocities $V_1 , V_2$

Any ideas would be helpful! Thanks!

Last edited: May 28, 2013
2. May 28, 2013

### barryj

I would think that given F(t), and the mass, you would integrate a(t) to find v(t) and then again to find d(t) distance a function of time. When you integrate a(t) you have the initial velocity given. Does the force act parallel to the plane?