Educator

Multi-Dimensional Kinematics

• In multiple dimensions, we realize some of the concepts we talked about before are actually vectors: displacement, velocity, and acceleration.
• Position is still location, we just now need to expand our coordinate system to have the right number of dimensions for whatever we are working on.
• Distance is still just a measure of length, but displacement is a vector describing the difference between two locations on our coordinate grid.
• Speed is still a question of "how fast", but velocity has to show direction as well as speed, so it must be a vector.
• Acceleration describes the change in velocity, so it must also be a vector.
• Gravity is an acceleration, so we now express it as a vector: →g=(0,  −9.8) [(m/s)/s]. Notice how there is no lateral gravity!
• Our formulas from before now must be modified to take vectors into account:
  

  → d   (t) = 1 2 → a   t2 + → vi   t + → di   .

• In one dimension we had v_f ² = v_i ² + 2a(∆d). Since it's meaningless to square a vector (remember, we can't multiply vectors together), we have to do this component-wise in multiple dimensions:
  

  vfx   2 = vix   2 + 2ax(∆dx)     &     vfy   2 = viy   2 + 2ay(∆dy)