What is the slope of a force vs. distance graph?

[JJBladester]

Homework Statement

What is represented by the slope of a Force vs. Distance graph?

Also, if I had a Force vs. Distance graph and knew my initial velocity was some value, how would I go about finding the velocity at any distance along the way?

Homework Equations

F=ma

W=Fd

v=d/t

The Attempt at a Solution

I know that the area under the curve of a Force vs. Distance graph represents work (W=Fd). Is the slope of a Force vs. Distance graph *acceleration*?

 

[LowlyPion]

Consider the units.

Units of Force = Newtons
Units of distance = meters

So the slope of an F/D plot would be N/m wouldn't it?

What do you know that has N/m as its units? Does anything spring to mind?

 

[JJBladester]

N = m∙kg/s²
m = m

N/m = kg/s² = surface tension (slope of Force vs. Distance graph)

Ok thanks for helping me think. Rise over run... Units of y-axis over units of x axis. That makes sense.

For the other part of my question, I think I've got it under wraps. To find the velocity at a certain distance of a Force vs. Distance graph, I need to:

Calculate area S below the graph.
This area is work, because it is equal to
S = integral of F(x)dx = integral of d(work)

Using conservation of energy I can now find the velocity:
S = Work = KE = 1/2 mv²