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solution14_pdf - arellano(aa39398 Homework 10...

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arellano (aa39398) – Homework 10 – weathers – (17101) 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 2 . 1 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 . 5 m , b = 2 . 3 m / s , d = - 2 . 4 m / s 2 , and e = 0 . 92 m / s 3 , with x in meters and t in seconds. Find the work done on the particle in the first 2 . 6 s of motion. Correct answer: 69 . 9087 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 . 3 m / s , and (1) v f = (2 . 3 m / s) + 2 ( - 2 . 4 m / s 2 ) (2 . 6 s) +3 (0 . 92 m / s 3 ) (2 . 6 s) 2 = 8 . 4776 m / s , (2) where t i = 0 s and t f = 2 . 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 (2 . 1 kg) bracketleftBig (8 . 4776 m / s) 2 - (2 . 3 m / s) 2 bracketrightBig = (75 . 4632 J) - (5 . 5545 J) = 69 . 9087 J . 002 (part 1 of 3) 10.0 points A 1560 kg car accelerates uniformly from rest to a speed of 13 . 4 m / s in 4 . 93 s. Find the work done by the net force on the car during this time interval Correct answer: 1 . 40057 × 10 5 J.
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