an objet undergoing contant acceleration is observed to pass through the origin

Question

an objet undergoing contant acceleration is observed to pass through the origin (0,0) of a 2d coordinate system at a time t=0s.at a time t=3s it had a velocity v=(8.5i-2.35j)m/s and at a timet=4.5s it had a velocity v= (-4.5i+5.6j)m/s
a)determine its constant acceleration vector (unit vectorform magnitude and direction)
b)determine the general form for the position vector as a function of time
c)the position vector at t=3s
d)its velocity vector at t=10s
e) its deplacement vector between 3 and 4.5s

Explanation / Answer

Whoa ... I think you might be confusing your "i"s. The "i" in "Vf=vi+at" should be a subscript and stands for "initial". The "i" that appears in the equation giving the initial velocity is a unit vector in the x direction. Were you clear on that? Yes, the initial position is at the origin, so that could be written as r = 0i + 0j. I think it would help if you tried to write your vector equations more carefully, in other words, be very careful about the directions that the vectors point in. The acceleration is in the y direction, but the initial velocity is in the x direction. So, does the acceleration change the value of the velocity in the x direction? What about the y direction? What is the initial velocity in the y direction? Maybe it would help you to write all your equations with both x and y components (i.e. include both the i and j unit vectors), even if one or both are zero. That would make it easier to see when you're mixing components incorrectly. Something like this: ri=rxiˆ+rxjˆ vi=vxiˆ+vyjˆ ai=axiˆ+ayjˆ where some of those components are equal to zero.

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