Finding Position of Object with Initial Velocity and Constant Acceleration

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SUMMARY

The discussion focuses on calculating the position of an object with an initial velocity of vo=(-14i-7j) m/s and a constant acceleration of a=(6i+3j) m/s² until it comes to rest. The key equations involved include acceleration a = dv/dt, which leads to the integration of velocity to find position. The object starts at the origin at t=0, and the solution requires applying calculus to derive the position function from the given initial conditions and acceleration. The main challenge discussed is the interpretation of the initial velocity components in the x and y directions.

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Homework Statement


An object, which is @ origin @ t=0, has an initial velocity
vo=(-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?!
 
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a = dv/dt
a*dt=dv
use some math(calculus)
v=dx/dt (x being position)

... now do you get an idea?
 

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