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So the centripetal force for a particle in uniform circular motion is mv^2/r. This also means that if F > mv^2/r than the particle will get closer to the center and if F < mv^2/r than it will travel further from the center.

Say a 5 kg object at point (0,5) on cartesian plane with initial speed of 10 ms

^{-1}and direction parallel to x-axis, a force of 35 N directed towards point (0,0) acts on the object. It no longer follows a circular path. So is it possible to get a equation that shows the motion of the object? Note the force is towards specific point (0,0) no matter where the object is.