{ 1 if t > 0 x(t) = { { 0 if t <= 0
If I remember my calculus correctly, x'(0) is undefined, while x(t) = 0. Does it therefore follow that at time t=0, the particle has a position and is moving but has no velocity? Would it be physically possible (i.e. compatible with the laws of physics as we currently understand them) for a particle with that behaviour to actually exist? -- SJK
In classical (non-quantum) mechanics a particle with mass cannot make such an instantaneous jump in position. It implies infinite acceleration which implies infinite force. So this case is not physically possible in classical mechanics (assuming zero-mass particles are not physically possible). -- Eob