Acceleration, Velocity, Position Vectors

Question

Acceleration vector = a(t) = (-cos(-t)) i + (-sin(-t)) j + (t) k , the initial velocity is v(0) = i + k , and the initial position vector is r(0) = i + j + k.

Find the velocity vector and position vector.

For the velocity vector, I got <(sin(-t) +1) , cos(-t) , (.5t^2) +1 >.

For the position vector, I got < -cos(t) + t + 1 , sin(-t) +1 , 1/6(t^3) + t + 1>.

It says that both of these are wrong, so if you could explain how you get to your answers, that would be helpful.

Answer 1

I'm assuming to get your answers you just integrated the acceleration vector to get the velocity vector and then integrated the velocity vector to get the position vector and used the initial velocity and position vectors to get the constants you get from integrating, which is all correct.

Where you went wrong is that I'm pretty sure the k dimension of the velocity vector should be -cos(-t) since substitution would make it positive and then integrating would make it negative again since the integral of sin is -cos. Also the i dimension of the position vector should be cos(-t) not cos(t). Everything else seems correct so just a couple minor errors were making your answers wrong