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9 - roofner(bar784 Homework 9 Weathers(17104 This print-out...

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roofner (bar784) – Homework 9 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A time-varying net force acting on a 4 . 5 kg particle causes the object to have a displace- ment given by x = a + b t + d t 2 + e t 3 , where a = 2 . 4 m , b = 2 . 2 m / s , d = - 3 . 4 m / s 2 , and e = 0 . 83 m / s 3 , with x in meters and t in seconds. Find the work done on the particle in the first 3 . 6 s of motion. Correct answer: 213 . 678 J. Explanation: Since the force is time dependent W integraldisplay x f x i vector F · dvectorx = integraldisplay x f x i m a dx = m integraldisplay x f x i d v dt dx = m integraldisplay x f x i d v dx d x dt dx = m integraldisplay v f v i v dv = 1 2 m v 2 f - 1 2 m v 2 i . Therefore work done on the particle is the change in kinetic energy. For this case, W = Δ K = K f - K i = 1 2 m ( v 2 f - v 2 i ) , where the velocity is found by differentiating the displacement: v = d x dt = b + 2 d t + 3 e t 2 v i = 2 . 2 m / s , and (1) v f = (2 . 2 m / s) + 2 ( - 3 . 4 m / s 2 ) (3 . 6 s) +3 (0 . 83 m / s 3 ) (3 . 6 s) 2 = 9 . 9904 m / s , (2) where t i = 0 s and t f = 3 . 6 s . Evaluation of the velocity at the initial and final times gives the desired result. W = K f - K i = 1 2 m ( v 2 f - v 2 i ) = 1 2 (4 . 5 kg) bracketleftBig (9 . 9904 m / s) 2 - (2 . 2 m / s) 2 bracketrightBig = (224 . 568 J) - (10 . 89 J) = 213 . 678 J . 002 (part 1 of 3) 10.0 points A 1650 kg car accelerates uniformly from rest to a speed of 10 . 3 m / s in 4 . 43 s. Find the work done by the net force on the car during this time interval Correct answer: 87524 . 2 J.
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