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Unformatted text preview: 1 Lecture 5 Motion in two and three dimensions Example of 2D motion: Projectile motion 2 y x r r f t = r v av Points in the direction of r r v The instantaneous velocity points tangent to the path. v f A particle moves along the blue path as shown. At time t 1 its position is r and at time t 2 its position is r f . 3 y x v r r f v f A particle moves along the blue path as shown. At time t 1 its position is r and at time t 2 its position is r f . v Points in the direction of v. t = v a av The instantaneous acceleration can point in any direction. 4 Define: Displacement Average velocity Instantaneous velocity dt d t t r r v = = lim t = r v av ( 29 ( 29 t t t r r r + = Position vector z y x r z y x + + = Velocity z y x z y x r v z y x v v v dt dz dt dy dt dx dt d + + = + + = = 5 z y x z y x r a z y x z y x 2 2 a a a dt dv dt dv dt dv dt d + + = + + = = Acceleration t...
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 Spring '11
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 Projectile Motion

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