# Find x dot as function of t

1. Sep 28, 2008

### commander

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

find velocity x dot, as function of time t, for particle mass m starts x=0, t=0
subject to force where Fo and c are constants.

Fx = Fo + ct

2. Relevant equations

x dot =Fo/m t + c/2m t^2

3. The attempt at a solution

obviously it is just an integration.
but how does the "m" get in there.

i know this is a simple question, but the solution eludes me

i have stuff like

Fo=c=constant
F=ma
F=mv dot = m r dotdot
d=r=vt=dv/dt
x dotdot = dv/dt = F/m = a = constant

what is Fx - is the the force component in direction x , or is it a vector , ?
what is Fo - a constant, vector?

how do you add in a t

Fx dt = Fo dt + ct dt

Fo = ma = m v dot

x dot = int Fo dt + int ct dt

= int dt + 1/2 c t^2
=

... and im lost

2. Sep 28, 2008

### gabbagabbahey

$$F_x$$ is the x-component of the total force on the particle and so

$$F_x=ma_x=m \ddot{x}=m \frac{d^2x}{dt^2}$$

Is that enough to get you started?

3. Sep 28, 2008

### commander

i think i got it .....

i did f=ma

a = f/m = x dot dot

so ....

x dot = ∫ Fo/m +∫ ct/m

is that the right method .....

4. Sep 28, 2008

### gabbagabbahey

Looks fine so far (I'm assuming you're integrating over dt). What do you get?

edit- make sure you include a constant of integration.