In Classical and Mechanical Physics, the mass of an object is constant when in it is in simple motion (no collisions and so forth). If the equation for Kinetic Energy is KE = (1/2)mv^2 and mass is constant, wouldn't that imply that the derivative of the Kinetic Energy in respect to velocity would be dKE/dv = mv? This would also state that the derivative of Kinetic Energy is momentum. I also found from another source that when considering v and v^2, KE is not a vector, whereas momentum is. I'd simply like clarification (while considering things in terms of Mechanical Physics). If the derivative is true, then what is the physical relationship between KE and momentum?