4 answersLast reply by: Professor Selhorst-Jones Thu May 9, 2013 4:54 PMPost by noha nasser on July 22, 2012wasn't the distance supposed to be equal to 7 which means that average speed will be equal to 7/2? :) 1 answerLast reply by: Professor Selhorst-Jones Thu Sep 6, 2012 4:46 PMPost by Nik Googooli on August 20, 2012wasn't the distance supposed to be equal to 7 which means that average speed will be equal to 7/2

### 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 vf 2 = vi 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)

## Multi-Dimensional Kinematics

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