Calculus: Can the velocity vs time graph ever curve?

Posted on 2015-10-13 06:15:00 in Physics by TYLER

F(X)=x^2 is my function for the distance vs time graph of a particle moving about in space. F'(X)=2x is the function for the velocity vs time graph.

2x is a linear relationship. The velocity vs time graph makes a straight line. Can it ever make a curve like my distance vs time graph (f(X)=x^2)?

And that would mean that the acceleration vs time graph would be like 2x. It wouldn't go straight across like it is now...

Maybe I should just ask this,

If the acceleration vs time graph is f''(X)=2x then what is the function of the distance vs time graph? It's something like something squared but then squared again

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