lecture05 - ACCELLERATION-Acceleration shows how fast...

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Unformatted text preview: ACCELLERATION-Acceleration shows how fast velocity changes- Acceleration is the velocity of velocity dt t v x x dt dx t x v t x v t t t lim dt t a v t v dt x d dt dv t v a t v a t t t 2 2 lim Examples: 2 2 2 / 10 ) ( / 10 2 / 5 ) ( s m dt dv t a t s m t s m dt dx t v ? ) ( ? ) ( / 5 ) ( 2 2 t a t v t s m t x Given: Given: ? ? / 10 ) ( 2 t x t v x v s m t a Solution: 1) Direct problem: 2) Inverse problem: Solution: 2 2 2 2 2 / 5 / 10 / 10 / 10 t s m dt t s m dt t v x x t s m dt s m dt t a v v t t t t t t Geometrical interpretation curve ) ( under area curve ) ( under area ) ( of curvature and ) ( of slope ) ( ) ( of slope ) ( t a v t v x t x t v t a t x t v t Positive Acceleration = a smile + t Negative Acceleration = a frown - x x Rain rule: a) At what time(s) is the velocity zero? 1. -1 s and +1 s 2. 0 s only 3. -2 s and +2 s only 4. -2 s, 0 s, and +2 s Questions: A particle is moving along the x-axis with the following position x versus time t:-1.5-1.0-0.5 0.0 0.5 1.0 1.5-2-1 1 2 x (m) t (s) b) During what time interval(s) is the velocity negative? 1. -2.5 s to -2 s and 0 s to 2 s 2. -1 s to +1 s 3. 2.5 s to -1 s and 1 s to 2.5 s c) During what time interval(s) is the acceleration positive? 1. -1 s to +1 s 2. -2.5 s to -1 s and 1 s to 2.5 s 3. -2 s to 0 s d) What is the average velocity v av-x between t 1 = 1 s and t 2 = 2 s?- 0.3 m/s v = slope of x ( t ) dt dx v 2 2 dt x d dt dv a a = slope of v ( t ) or a = curvature of x ( t ) t t t x v a x Change in velocity = area under a ( t ) curve dt a v t t 1 dt v x t t 1 Displacement = area under v ( t ) curve v v t t 1 t t t x v a 1. speeds up all the time1....
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lecture05 - ACCELLERATION-Acceleration shows how fast...

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