# Lec-04 - MOTION IN TWO (OR MORE) DIMENSIONS Learning...

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1 [©2008 RJ Bieniek] M OTION IN T WO ( OR MORE ) D IMENSIONS Learning Objectives After you complete the homework associated with this lecture, you should be able to: Understand the physical meaning and mathematical definition of vector position , displacement , velocity , and acceleration in two-dimensional situations. Analyze and predict characteristics of two-dimensional motion using this understanding. Determine the path of objects undergoing constant acceleration (e.g., free-fall trajectories). 2 [©2008 RJ Bieniek] P v ' d P r dt v x ˆ i % v y ˆ j ' dx dt ˆ i % dy dt ˆ j Y v x ' dx dt v y ' dy dt Two Dimensional (2-D) Motion Particle has position vector r P = r x i ^ + r y j ^ = x i ^ + y j ^ . It moves to another position if it has a velocity v P : 3 [©2008 RJ Bieniek] I I NSIGHT NSIGHT : Multiplying both sides of by dt d P r dt ' P v gives d r P = v P dt . A small change in the position vector occurs in the direction of the velocity vector , with the small increment in time

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## This document was uploaded on 09/02/2009.

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Lec-04 - MOTION IN TWO (OR MORE) DIMENSIONS Learning...

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