Finding Position of Object with Initial Velocity and Constant Acceleration

[moondawg]

Homework Statement

An object, which is @ origin @ t=0, has an initial velocity
v_o=(-14i-7j)m/s
and constant acceleration
a=(6i+3j)m/s²
Find position of the object when it comes to rest.

Homework Equations

The Attempt at a Solution

So i understand how to solve this problem if the -14 is the initial vel in the x direction or and -7 is the vel in the y direction but I'm not sure if that is what that equation means or if I am supposed to find the resultant and use that? I'm pretty sure the first suggestion is what we did in class but can someone please verify so I can do this problem correctly?!

 

[The legend]

a = dv/dt
a*dt=dv
use some math(calculus)
v=dx/dt (x being position)

... now do you get an idea?