Rocket; velocity and postion vectors

[masterstakes]

Homework Statement

A faulty model rocket moves in the xy-plane. The rocket's acceleration has components: ax(t) = 2.5t² and ay(t) = 9 - 1.4t
At t= 0, the rocket is at the origin and has velocity V0 = 1i + 7j
(a) calculate the velocity and positions vectors as functions of time
(b) What is the max height rreached by the rocket?
(c) What is the horizontal displacement of the rocket when it returns to y = 0?

Homework Equations

The Attempt at a Solution

well, I am not sure where to start.
perhaps take the antiderivitives of the accelerations functions until you get time or velocity?
then plug in those answers to the velocity vector?

 

[fzero]

The Attempt at a Solution

well, I am not sure where to start.
perhaps take the antiderivitives of the accelerations functions until you get time or velocity?
then plug in those answers to the velocity vector?

You're correct that you have to integrate the acceleration functions to get the velocity and then displacement. However you don't quite "plug in those answers to the velocity vector," rather you are told v(t=0) and r(t=0). You will use those values to determine the integration constants.