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Chapter II Mechanics A. Streight-line motion, average and instantaneous x- B. C. D. E. velocity Streight-line motion with constant acceleration Freely falling bodies Projectile motion Uniform Circular motion A. Streight-line motion, average and instantaneous x-velocity 1. Average Velocity s = distance r = displacement y t1 r1 A s r r2 0 The displacement of a particle is deﬁned as its change in position. B t2 x Magnitude of Average velocity Average Speed The average speed of a particle, a scalar quantity, is deﬁned as the total distance traveled divided by the total time it takes to travel that distance The average velocity of a particle is deﬁned as the particle’s displacement r divided by the time interval t during which that displacement occurred 2. Instantaneous Velocity Instantaneous velocity v equals the limiting value of the ratio r/t as t approaches zero Magnitude of Instantaneous velocity = Instantaneous Speed The instantaneous speed of a particle is deﬁned as the magnitude of its velocity 3. Acceleration The average acceleration of the particle is deﬁned as the change in velocity v divided by the time interval t B. Streight-line motion with constant acceleration C. Freely Falling Bodies reference h y = -h yo = 0 vo = 0 =-g - h = 0 + 0 t + ½(- g) t2 -h = - ½ g t2 h = ½ g t2 For example, look exercise number 2.44 at page 87 (66) A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground. After it is released, the sandbag is in free fall. (b) How many seconds after its release will the bag strike the ground? D. Projectile motion y vox = vo cos α voy = vo sin α y-direction v = voy + at = vo sin α + at y = voy t + ½ a t2 = vo t sin α + ½ a t2 vo voy 0 α vox x-direction v = vox = vo cos α x = vox t = vo t cos α x E. Uniform Circular Motion v2 R v v1 r2 r1 v2 v1 r2 r as r1 R = circular radius as = centripetal acceleration t = time interval