W2.2 - January 11, 2008 Physics for...

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Unformatted text preview: January 11, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2008 Lecture 6 January 11, 2008 Physics for Scientists&Engineers 1 2 Acceleration Vector Acceleration Vector Average acceleration = change of velocity during a given time interval Instantaneous acceleration vector Acceleration vector is the second derivative of the position vector a x = ! v x ! t a x ( t ) = lim ! t " a x = lim ! t " ! v x ! t # dv x dt a x ( t ) = d dt v x = d dt d dt x ! " # $ % & = d 2 dt 2 January 11, 2008 Physics for Scientists&Engineers 1 2 Acceleration Vector Acceleration Vector Average acceleration = change of velocity during a given time interval Instantaneous acceleration vector Acceleration vector is the second derivative of the position vector a x = ! v x ! t a x ( t ) = lim ! t " a x = lim ! t " ! v x ! t # dv x dt a x ( t ) = d dt v x = d dt d dt x ! " # $ % & = d 2 dt 2 x January 11, 2008 Physics for Scientists&Engineers 1 3 Example: Velocity & Acceleration Example: Velocity & Acceleration Graph of and Acceleration: v x ( t ) = ! 10.1 m/s + (2.2 m/s)( t /s) x ( t ) = 17.2 m ! (10.1 m)( t /s) + (1.1 m)( t /s) 2 a x ( t ) = 2.2 m/s 2 a x [m/s 2 ] January 11, 2008 Physics for Scientists&Engineers 1 4 Example: 100 m Sprint Example: 100 m Sprint Carl Lewis World Record, 1991 World Championship v x = ! x ! t = x f " x i t f " t i a x = ! v x ! t = v xf " v xi t f " t i Fit: v x = 11.58 m/s http://www.youtube.com/watch?v=2MvNIBeUb90 January 11, 2008 Physics for Scientists&Engineers 1 5 Inverse Relationships Inverse Relationships Start with the definition v x =dx/dt and integrate both sides:...
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W2.2 - January 11, 2008 Physics for...

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