For motion in a straight line with constant acceleration, the displacement is given by x=x0+v0t+21at2, where the symbols have their usual meanings.
(i) Starting from the above relation, derive an expression for the instantaneous velocity v as a function of time.
(ii) Show explicitly that the instantaneous velocity equals the time derivative of the position function.
(iii) Prove that, for uniform motion (a=0), the instantaneous velocity is equal to the average velocity for any chosen time interval.
(iv) Give a physical explanation of why, when a=0, the average velocity over a finite interval differs from the instantaneous velocity at an instant within that interval.