I have a problem for uni that I don't really know how to approach. The problem is:
"The velocity of a particle at time t = v(t) = sinti + costj - 10tk. What is the particle's acceleration, a(t) = dv/dt as a function of time? Given that at t = 0 the particle is at (1,0,0), find its position at time t."
I understand the relationship between position, velocity and acceleration. i.e. - If x(t) is the position at time t, then the velocity v(t) = dx/dt and the acceleration a(t) = dv/dt. What I don't understand is how to treat the i, j and k in the expression? Just for my own sanity I'm thinking of t like I'd usually think about an x variable, but are i, j and k supposed to be treated as constants? If they didn't exist, I'd have no problem integrating/differentiatiating, but their occurence has completely thrown me off. Any help would be greatly appreciated.