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hw4 - lenoir(wml297 oldhomework 04 Turner(58220 This...

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lenoir (wml297) – oldhomework 04 – Turner – (58220) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points The velocity v ( t ) of some particle is plotted as a function of time on the graph below. The scale on the horizontal axis is 3 s per division and on the vertical axis 5 m / s per division. Initially, the particle is at x 0 = 35 m. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 v ( t ) time ( × 3 s) velocity ( × 5 m / s) What is the position x of the particle at time t = 12 s? Correct answer: 185 m. Explanation: Looking at the v ( t ) plot we see that over time t = 4 (3 s) = 12 s, the particle’s velocity decreases from the initial v 0 = 4 (5 m / s) = 20 m / s to final v f = 1 (5 m / s) = 5 m / s . The v ( t ) line is straight, which indicates constant deceleration rate, so the average velocity is given by ¯ v = v 0 + v f 2 = 20 m / s + 5 m / s 2 = 12 . 5 m / s , the particle’s displacement is Δ x = t · ¯ v = (12 s) (12 . 5 m / s) = 150 m , and its final position x = x 0 + Δ x = 35 m + 150 m = 185 m . 002 (part 2 of 2) 10.0 points What is the particle’s acceleration? Correct answer: - 1 . 25 m / s 2 . Explanation: The average acceleration of the particle is ¯ a = Δ v Δ t = v f - v 0 t = 5 m / s - 20 m / s 12 s = - 1 . 25 m / s 2 Since the v ( t ) line is straight, the acceleration is constant, so a = ¯ a = - 1 . 25 m / s 2 . 003 (part 1 of 2) 10.0 points A speeder passes a parked police car at 31.6 m/s. Instantaneously, the police car starts from rest with a uniform acceleration of 2.46 m/s 2 . a) How much time pases before the speeder is overtaken by the police car? Correct answer: 25 . 6911 s. Explanation: Basic Concepts: For the speeder, Δ x s = v s Δ t For the policeman, v i = 0 m/s, so the equa- tion simplifies to Δ x p = 1 2 a p t ) 2 Let : v s = 31 . 6 m / s v i,p = 0 m / s a p = 2 . 46 m / s 2 .
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