Changing V(x) to V(t): Chain Rule Application?

[StephenSF8]

I have a function for velocity, V in terms of position, x. The equation is of the form V(x) = a*x²+b*x+c. Initial conditions are x=0, t=0.

How do I change from V(x) to V(t)? It seems this would be an application of the chain rule, dy/dx = dy/du * du/dx, but I'm struggling to adapt it to this situation. Am I way off base?

Thanks!

 

[mathman]

Assuming t means time, then V=dx/dt. So dt = dx/(a*x²+b*x+c). Integrate both sides to get t as a function of x. Solve for x as a function of t. Then take the derivative to get V. Good luck!

 

[mateomy]

Velocity is the result of differentiating a position equation. To reverse that you have two options, (the same pretty much): Integrate or find the Antiderivative.

Enjoy.

 

[StephenSF8]

Assuming t means time

You assume correct.

Integrate both sides to get t as a function of x. Solve for x as a function of t.

This is what I was missing. I was able to perform the integration and solve for x and all is well. Thanks for the help!