Re: Axis Transformation, time -> distance

AI Thread Summary
To transform a Force vs. Time graph into a Force vs. Distance graph, the equation distance = 1/2(F/mass)*(t^2) is applicable only under the assumption of constant force. However, the relationship between distance and time is generally more complex, requiring integration of force over time. The correct approach involves using the integral of force divided by mass to account for varying forces. This complexity highlights the need for careful consideration in the transformation process. Accurate plotting depends on understanding these underlying principles.
miloko
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Hi all,

I have a graph, plotted as Force vs. Time. Now, I want to plot the graph as Force vs. Distance. I'm taking distance = 1/2(F/mass)*(t^2). I think this is the right way to do it, but just need some confirmation.

Thanks,
Mike
 
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That would work only if the force is constant. Generally, the relation between distance and time is a bit more complicated:

x-x_0 = v_0 t + \int_{0}^{t}\int_{0}^{t'}\frac {F(t'')}{m}dt'' dt'
 
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