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Unformatted text preview: Solution for Long-answer Homework 5 Inertia II, inclined plane problem Solution to Long-answer Homework Problem 5.1(Acceleration from graph) Problem: For the following velocity graph, velocity is in m / s and time is in s . For the interval t = 2s to t = 5s , find (a)the instantaneous acceleration, and (b)the displacement Δ x . 1 2 3 4 5 1 2 3 4 5 v t Solution to Part (a) The instantaneous acceleration (which is constant over the interval) is simply the slope of v ( t ) (rise over run). rise run = 3m / s 3s = 1 m s 2 . Grading Key: Part (a) 3 Points Solution to Part (b) Displacement will be the area under the curve. Counting, this comes out to be 7 . 5m (see figure). Or, of course, you could figure out what the function is in that interval and integrate it. Δ x = integraldisplay Δ t v ( t ) dt = integraldisplay 5 2 t- 1 dt = parenleftbigg 1 2 t 2- t parenrightbiggvextendsingle vextendsingle vextendsingle vextendsingle 5 2 = 15 2 = 7 . 5m 1 2 3 4 5 1 2 3 4 5 v t Grading Key: Part (b) 3 Points Total Points for Problem: 6 Points 1 Solution to Long-answer Homework Problem 5.2() Problem: You step outside one winter day to get the newspaper, right at the street. Your driveway, from the door to the newspaper, is 8 meters long, and completely iced over. The angle of incline of your driveway is 10 ◦ . You take your first tentative step, and suddenly find yourself sliding down the driveway on your bum (assume you start from rest). (a)What is your acceleration as you slide down the driveway? (b)How long does it take to get to the street? (c)Once you get to the bottom, you can’t stop yourself from sliding. What is your speed at this instant? (d)You then slide out into the street which is a little less icy, so you experience an acceleration opposite the direction of motion of . 5 m s 2 . How long does it take you to stop, from the instant you slide into the street? (e)How far do you travel in this time? Solution to Part (a) Let me choose down the driveway to be positive. Your driveway’s angle of incline is 10 ◦ , thus by equation 4.39 your acceleration as you slide down the driveway is: a θ = g sin θ = (9 . 8 m s...
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