Solving Motion Equations with Integration

AI Thread Summary
The discussion focuses on solving motion equations through integration, specifically addressing confusion around setting components to zero. The initial attempt to derive position using integration led to unreasonable time values when incorrectly setting the j-component to zero. Clarification was provided that the y=0 corresponds to the x-axis, not the y-axis. After correcting the approach and applying the quadratic formula to the x-component, the participant successfully found a solution. The conversation highlights the importance of accurately interpreting the components in motion equations.
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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.
 
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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.
 
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!
 
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