Assume an object accelerating at a certain value dV/dt. If this object was traveling in a circular motion the centripetal force would increase as the object moves faster. 
To maintain centripetal acceleration constant while the object is accelerating (in its forward motion dV/dt) I think it would need to follow some sort of spiral path so that after a certain time the object would be traveling faster however the radius also increases.

Does anybody know what type of spiral would keep centripetal acceleration constant? What formula would this spiral have?

Thanks in advance for the help.

It sounds like you are looking for what we now call the Archimedean spiral (He studied spirals in general and published a book about them).

This one moves away from a fixed point with contant speed along a line which rotates with fixed velocity about the fixed point.

 

If we set the origin at the fixed point, the equation is

[math]r = a\theta [/math]

 

 

34 minutes ago, Ale89 said:

 Does anybody know what type of spiral would keep centripetal acceleration constant? What formula would this spiral have?

A circle is one solution

Swansont, I meant: a spiral to keep centripetal accerleration constant while the object accelerates at a certain value forwards (constant tangential acceleration). Sorry for not being precise in my final question.

Further Studiot, I dont think the archemedian sprial will keep centripetal acceleration constant while the object is accelerating tagentaly. This is because the change in radius over time (dr/dt) is not constant to keep the centripetal accerleration constant, and the archemedian spiral assumes a constant increase in radius between turning points at a constant angular velocity therefore in the archemedian spiral dr/dt=constant.