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SPEED and VELOCITY Speed is how far an object travels in a given time period. Speed is how far an object travels in a given time period. S= d/tS= d/t Speed is a scalar quantitySpeed is a scalar quantity Velocity is the rate at which displacement changes Velocity is the rate at which displacement changes V= Δd/ΔtV= Δd/Δt Velocity is a vector quantity.Velocity is a vector quantity. Uniform Motion occurs when the speed and the direction of a moving body remains the same. Uniform Motion occurs when the speed and the direction of a moving body remains the same.

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Average vs. Instantaneous Velocity Average velocity is the change in displacement over the given time interval. On a displacement-time graph the slope of the line connecting the initial and final positions Instantaneous velocity is the velocity of the object at any given time. On a displacement-time graph the slope of the tangent line (due to the limit theory)

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Sample Problem If a car travels east for a 12 km in a time of 3 minutes, what is the cars average velocity? If a car travels east for a 12 km in a time of 3 minutes, what is the cars average velocity? V=Δd/Δt V=Δd/Δt Δd= 12 kmΔd= 12 km Δt = 3 minutesΔt = 3 minutes V= 12 km/ 3min = 4km/minV= 12 km/ 3min = 4km/min

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Sample Problem 2 An airplane is traveling at a velocity of 245km/ min east. How far will it travel in two hours? d= Δv* Δt Δv=245km/min Δt=2hr * 60 min = 120 min d= 245 km/hr * 120 min = 30480 km

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ACCELERATION Acceleration is the rate at which the velocity of a body changes. Acceleration is the rate at which the velocity of a body changes. Formula Formula a= v f - v i / Δta= v f - v i / Δt V f = final veloictyV f = final veloicty V i = initial velocityV i = initial velocity

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Sample Problem What is the acceleration of a car whose velocity increases from15 m/s to 25 m/s in 5 s. What is the acceleration of a car whose velocity increases from15 m/s to 25 m/s in 5 s. v f= 25 m/sv i = 15 m/s Δt=5s v f= 25 m/sv i = 15 m/s Δt=5s a=(25-15)/5= 10m/s/5s= 2m/s 2 a=(25-15)/5= 10m/s/5s= 2m/s 2

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Sample problem 2 An airplane is flying at 60 m/s accelerated uniformly at the rate of 0.50 m/s2 What is the speed at the end of 10s. Vi= 60m/sa=0.50m/s2Δt =10 s If a= vf- vi / Δt then vf =vi + a Δt vf =60m/s + ( 0.50m/s2 )(10 s) Vf = 60 m/s + 5 m/s = 65 m/s

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EQUATIONS V=Δd/Δt V=Δd/Δt d= Δv* Δt d= Δv* Δt a= v f -v i / Δt a= v f -v i / Δt v f =v i + a Δt v f =v i + a Δt V= (V F + V I ) /2 V= (V F + V I ) /2 d= V I Δt + 0.5a(Δt) 2 d= V I Δt + 0.5a(Δt) 2 (V f ) 2 – (V i ) 2 = 2 ad (V f ) 2 – (V i ) 2 = 2 ad

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