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1998MT1s

# 1998MT1s - Physics 125 Test I Solutions 1(15 points...

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Physics 125 Test I September 29, 1998 Solutions 1. (15 points) Kinematics The motion of a particle is given by k t z j t y i t x t r ˆ ) ( ˆ ) ( ˆ ) ( ) ( + + = r where x(t) = 10.0 m y(t) = 5.0 + 10.0t m z(t) = 20.0 – 10.0t –5t 2 m a). (5 points) Find the velocity V r . Use vector notation. t dt dz dt dy dt dx 0 . 10 0 . 10 0 . 10 0 . 0 - - = = = k t j V ˆ ) 0 . 1 ( 0 . 10 ˆ 0 . 10 + - = r m/s b). (5 points) Find the acceleration a r . Use vector notation. k dt V d ˆ 0 . 10 - = r m/s 2 c). (5 points) Find the speed (i.e. the absolute magnitude of the velocity) at t = 3.0 seconds. s m V V V V V V z y x / 2 . 41 ˆ 40 10 2 2 2 2 2 = + = + + = r r (2 point off if units missing) 2. (20 points) One-D motion. A long massless string with three balls (initially at rest) tied to it at intervals is dropped. (Newton’s Balls). If the first ball is 19.6 cm from

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the ground, the second is 78.4 cm from the ground and the third is 176.0 cm from the ground, find a). (5 points) the time it takes for the first ball to hit the ground, h 1 = 19.6 cm g=980 cm/s 2 g h t gt h 2 2 1 2 1 = = since v = 0 initially t 1 = 0.2 s b) (5 points) the time interval between the first and second ball hitting the ground, h 2
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1998MT1s - Physics 125 Test I Solutions 1(15 points...

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