# HW#2 - Math 293 Homework 2 Problem 1.2 17 Solution If a t =...

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Unformatted text preview: Math 293 Homework 2 Problem 1.2 17. Solution : If a ( t ) = ( t + 1) − 3 , then v ( t ) = integraldisplay 1 ( t + 1) 3 dt =- 1 2 1 ( t + 1) 2 + C 1 . Since v (0) = 0 , we have C 1 = 1 2 . Hence x ( t ) = integraldisplay bracketleftbigg- 1 2 1 ( t + 1) 2 + 1 2 bracketrightbigg dt =- 1 2 1 ( t + 1) 1 + 1 2 t + C 2 . Since x (0) = 0 , we have C 2 =- 1 2 . Therefore x ( t ) = 1 2 bracketleftbigg 1 ( t + 1) 1 + t- 1 bracketrightbigg . 43. Solution : The velocity and position function for the spacecraft are v S ( t ) = 0 . 0098 t and x S ( t ) = 0 . 0049 t 2 , and the corresponding functions for the projectile are v P ( t ) = c 10 = 3 × 10 7 and x P ( t ) = 3 × 10 7 t . The condition that x S = x P when the spacecraft overtakes the projectile gives . 0049 t 2 = 3 × 10 7 t , whence t = 3 × 10 7 . 0049 = 6 . 12245 × 10 9 sec = 6 . 12245 × 10 9 3600 × 24 × 365 . 25 = 194 years . Since the projectile is traveling at 1 / 10 the speed of light, it has then traveled a distance of about 19 . 4 light years, which is about 1 . 8376 × 10 17 meters....
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HW#2 - Math 293 Homework 2 Problem 1.2 17 Solution If a t =...

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