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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 ˆ ˆ ˆ z y x + + = Velocity z y x z y x r v ˆ ˆ ˆ ˆ ˆ ˆ z y x v v v dt dz dt dy dt dx dt d + + = + + = = 5 z y x z y x r a ˆ ˆ ˆ ˆ ˆ ˆ 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
 Staff
 Acceleration, Projectile Motion, Velocity, DT DT DT

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