Question

The equations of motion of a point particle in space are given by:
(i) x(t) = 2t2 − 3 ; y(t) = −3t2 ; z(t) = 4t2 − 5
(ii) x(t) = asin(ωt); y(t) = acos(ωt); z(t) = bt
In each case, calculate the velocity vector and the acceleration vector for an arbitrary value of t (considering a and ω as fixed parameters). Calculate the absolute values of those vectors.