A car starts moving from rest on a horizontal ground such that the position vector of car with respect to its starting point is given as `vec(r) = b t hat(i) - c t^(2) hat(j)`, where a and b are position constants, direction (x and y axes) intersect at the starting point of car (origin). Find:
(a) The equation of the trajectory of car `y = f(x)`.
(b) The angle between direction of velocity and acceleration of car as a function of time `theta = f (t)`.
(c) Average velocity of car over first t seconds of motion