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Final Velocity after Any Displacement The Last Equation… For now The Last Equation • If we take the equations that we’ve looked at so far, and do some mathematical hand waving… • We get: vf 2 2 vi 2 a x Example • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75m? Example • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75m? • Givens: a= 0.500 m/s2 vi= 0 m/s Δx=4.75 m vf= ? Example • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75m? • Givens: a= 0.500 m/s2 vi= 0 m/s Δx=4.75 m vf= ? vf 2 2 vi 2 a x Example • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75m? • Givens: a= 0.500 m/s2 vi= 0 m/s Δx=4.75 m vf= ? vf vf vf 2 vi 2 a x 2 2 ( 0 m / s ) 2 ( 0 . 500 m / s )( 4 . 75 m ) 2 4 . 75 m / s 2 vf 2 2 2 2 4 . 75 m / s 2 2 . 18 m / s Practice • Pg. 58 Practice E Falling Objects vf 2 2 vi 2 a y Same Equation, Different Direction A new given… • When an object falls straight down it is in Free Fall. • Objects in Free Fall always have the same acceleration- the acceleration of gravity (g). • a= -9.8 m/s2 (this will ALWAYS be ‘a’ for a ‘falling’ object- either thrown up or falling down) Positive and Negative • Variables that are Negative are in the Downward direction. • Variables that are Positive are in the Upward direction. a= -9.8m/s2 -Δy Example • Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor? Example • Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor? • Givens: a=-9.8m/s2 vi=6.0m/s Δy= -2.0m t=? Example • Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor? • Givens: a=-9.8m/s2 vi=6.0m/s Δy= -2.0m t=? v f v i at vf 2 2 vi 2 a y We can’t solve for t right away, so use a 2-step process. Step1- Find vf Step 2- Find t Practice • Pg 63, Practice F