I'm confused about what situations you should use unit vectors in... and it seems that when I approach the same problem using unit vectors vs. without unit vectors, I get different answers. Why? To illustrate my confusion, here's an example that I tried solving using unit vectors, and without unit vectors. For example: 1. The problem statement, all variables and given/known data A particle moves in the xy plane from the origin at t=0 with an initial velocity having an x-component of 20m/s, and a y-component of -15m/s. The particle has an acceleration in the x-direction of ax=4m/s2 What is the velocity of the particle at 5 seconds? 2. Relevant equations Velocity as a function of time: vf=vi+at 3. The attempt at a solution Expressed as unit vectors: vf = (vix+axt)i + (viy+ayt)j vf = (20+4t)i - 15j vf = [20 +4(5)]i - 15j = (40i - 15j)m/s Expressed into x and y components: vfx=40m/s, vfy=-15m/s vf = sqrt(402 + (-15)2) = 37m/s Expressed as "regular" vectors: x direction: vfx = vix+axt = 20+4t y direction: vfy = viy+ayt = -15 +4(0) = -15 vf = sqrt[(20+4t)2 + (-15)2] = sqrt(625 + 160t + 16t2) = 43m/s EDIT: I rechecked my calculations, and realized that my final answer for the unit vector approach is also 43m/s... D'oh! Given my mistake, my question is now: Will a unit vector approach always give me the same answer as when I don't use unit vectors?