Can velocity of the free particle remain constant in non-inertial frame as contrast to free particle in an inertial frame? I know the answer is straightforward yes but taking a different perspective that non-inertial frames are frames where space is non-homogenous,and anistropic and time is non-homogenous. Then we can argue that lagrangian of free particle may/may not depend on coordinate of particle but definitely depend on velocity and time,which by Euler-Lagrange equations suggest velocity should not be constant,now how to answer the question?
closed as unclear what you're asking by alephzero, John Rennie, Jon Custer, glS, Qmechanic♦ Jun 11 at 7:32
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Consider two objects falling from the same height. One is dropped without initial velocity. The second is thrown downwards with some initial vertical velocity vo. The velocity of the second object relative to the first one (non inertial frame) is vo during the entire fall.