This question emphasizes geometry and should be done without use of a coordinate system. It should also be done using only symbolic manipulation of vectors. Here it is.
Consider a particle moving with a constant, non-relativistic velocity. Starting with a general expression for kinetic energy in terms of either velocity or momentum, prove that the particle need not be under the influence of a non-zero net force. Do not refer to a coordinate system. Your argument must be stated in words as well as mathematically.
I’m not entirely happy with the way I articulated the question. I’m open to suggestions for improvement, but I want the question to have an air of vagueness about it.