# W2.3 - Physics for Scientists Engineers 1 Spring Semester...

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January 11, 2008 1 Engineers 1 Engineers 1 Spring Semester 2008 Lecture 7

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January 11, 2008 2 Position, velocity and acceleration vectors Position, velocity and acceleration vectors Related through derivatives and integrals x ( t ) ! v x ( t ) = dx ( t ) dt ! a x ( t ) = dv x ( t ) dt x ( t ) = x 0 + v x ( t ') dt ' 0 t ! " v x ( t ) = v x 0 + a x ( t ') dt ' 0 t ! " a x ( t )
January 11, 2008 3 Summary: Five Kinematical Equations Summary: Five Kinematical Equations One-dimensional motion with constant acceleration : Can solve practically all one-dimensional problems v x ( t ) = v x 0 + at x ( t ) = x 0 + v x 0 t + 1 2 a x t 2 v x = 1 2 [ v x 0 + v x ( t )] x ( t ) = x 0 + v x t v x ( t ) 2 ! v x 0 2 = 2 a x [ x ( t ) ! x 0 ]

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January 11, 2008 4 Free Fall Free Fall Particular motion with constant acceleration in 1 d a x = - g, with g = 9 . 81 m/s 2 Conventional notation: call vertical axis y axis Kinematic equations for this case v y ( t ) = v y 0 ! g t y ( t ) = y 0 + v y 0 t ! 1 2 g t 2 v y = 1 2 [ v y ( t ) + v y 0 ] y ( t ) = y 0 + v y t v y ( t ) 2 ! v y 0 2 = ! 2 g [ y ( t ) ! y 0 ] x y Use those for constant acceleration: (Substitution: y for x, -g for a x )
January 11, 2008 5 Studying Free Fall with Studying Free Fall with a Computer a Computer We can study free fall using a computer In the movie to the right, we use a computer to study free fall We release the computer from rest at a height of 12.7 m The computer undergoes free fall

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6 Studying Free Fall with Studying Free Fall with a Computer (2) a Computer (2) We digitized the frames (30 frames per second) The yellow curve is drawn using the equation y = 12.7 m ! 1
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W2.3 - Physics for Scientists Engineers 1 Spring Semester...

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