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Unformatted text preview: lim (kl9356) – Homework 9 – Weathers – (17104) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A timevarying net force acting on a 2 . 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 . 2 m , b = 3 . 1 m / s , d = 4 . 4 m / s 2 , and e = 2 m / s 3 , with x in meters and t in seconds. Find the work done on the particle in the first 2 . 5 s of motion. Correct answer: 420 . 437 J. Explanation: Since the force is time dependent W ≡ integraldisplay x f x i vector F · dvectorx = integraldisplay x f x i ma dx = m integraldisplay x f x i dv dt dx = m integraldisplay x f x i dv dx dx dt dx = m integraldisplay v f v i v dv = 1 2 mv 2 f 1 2 mv 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 = dx dt = b + 2 dt + 3 et 2 v i = 3 . 1 m / s , and (1) v f = (3 . 1 m / s) + 2 ( 4 . 4 m / s 2 ) (2 . 5 s) +3 (2 m / s 3 ) (2 . 5 s) 2 = 18 . 6 m / s , (2) where t i = 0 s and t f = 2 . 5 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 . 5 kg) bracketleftBig (18 . 6 m / s) 2 (3 . 1 m / s) 2 bracketrightBig = (432 . 45 J) (12 . 0125 J) = 420 . 437 J . 002 (part 1 of 3) 10.0 points A 1850 kg car accelerates uniformly from rest to a speed of 11 . 4 m / s in 3 . 25 s....
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This note was uploaded on 09/07/2010 for the course PHYS 1710 taught by Professor Weathers during the Fall '08 term at North Texas.
 Fall '08
 Weathers
 Magnetism, Force, Work

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