ENG102_SL1

# ENG102_SL1 - DATE: DUE: ENG102, Solution to homework set...

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DATE: September 26, 2011 DUE: September 30, 2011 ENG102, Solution to homework set #1. 1. After Sample Problem 2/4 in Text: A freighter is moving with a speed of v (0) = 8 knots when its engines are suddenly stopped. If it takes t 10 = 10 minutes for the freighter to reduce its speed to v ( t 10 ) = 4 knots, determine and plot the speed v ( t ) and position s ( t ) (with s (0) = 0 ) as a function of the time t during this interval. a. Answer the questions above for the acceleration a = - kv ; determine k in the process. We have the equation of motion ˙ v = - kv (1) v ( t ) = C exp( - kt ) (2) Using the two conditions, we determine C and k from v (0) = 8 knots and v ( 1 6 h ) = 4 knots : C = 8 knots (3) k = 6 ln 2 h - 1 (4) which give us the solution v ( t ) = 8 knots exp( - 6 ln 2 t/h ) (5) s ( t ) = Z t 0 v ( t ) dt = 4 mi 3 ln 2 (1 - exp( - 6 ln 2 t/h )) (6) b. Answer the questions above for the acceleration a = - kv 3 ; determine k in the process. We have the equation of motion ˙ v = - kv 3 (7)

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## This note was uploaded on 12/18/2011 for the course ENG 102 taught by Professor Eke during the Fall '08 term at UC Davis.

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ENG102_SL1 - DATE: DUE: ENG102, Solution to homework set...

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