The position of a particle is given by r = (at2)i + (bt3)j + (ct -2)k, where a, b, and c are constants.

Answer 1

We're given

r = at²i + bt³j + ct^–2k

but what is the question? Probably we would be asked for velocity

v = dr/dt = 2ati + 3bt²j – 2ct^–3k

and acceleration

a = dv/dt = 2ai + 6btj + 6ct^–4k.

The exercise would be to use the rules of differentiation with variable t and all other symbols constant.