Unformatted text preview: v ( t ) = 95 . 65 + Ce − t/ 10 . Since v (0) = 0, we Fnd C = − 95 . 65 and, hence, v ( t ) = 95 . 65 − 95 . 65 e − t/ 10 . Integrating yields x ( t ) = 95 . 65 t − 956 . 5 e − t/ 10 + C 1 . Using the fact that x (0) = 0, we Fnd C 1 = − 956 . 5. Therefore, the equation of motion of the object is x ( t ) = 95 . 65 t − 956 . 5 e − t/ 10 − 956 . 5 . To determine when the object is traveling at the velocity of 70 m/sec, we solve v ( t ) = 70. That is, 70 = 95 . 65 − 95 . 65 e − t/ 10 = 95 . 65 ( 1 − e − t/ 10 ) ⇒ t = − 10 ln ± 1 − 70 95 . 65 ² ≈ 13 . 2 sec . 128...
View
Full Document
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Buoyancy, Force, Kilogram

Click to edit the document details