Solving Motion Equations with Integration

[runningphysics]

Homework Statement

A particle leaves the origin with its initial velocity given by v⃗ 0=14i+13jm/s, undergoing constant acceleration a⃗ =−1.3i+0.26j m/s2. Find when and where the particle crosses the y axis.

Relevant Equations

Δx=V_0 t+1/2 at^2
and other kinematics equations

I'm not sure where to start, when I tired using integration of the initial equation to get pos(t)=-.65t^2 i + .13t^2 j + 14ti +13tj but after separating each component, i and j, and setting j equal to zero I got 0 or -100 seconds which doesn't seem like a reasonable answer.

 

[Orodruin]

First, you do not set j = 0. I assume you mean setting the j-component to zero.

Second, y=0 is the x-axis, not the y-axis. The y-axis corresponds to x=0.

 

[runningphysics]

OK, I tried it out and it works! I was confused with the wording of the question, but setting the x equation, x=-.65t^2 i + 14t i, equal to zero and using the quadratic worked. Thanks for your help!