Brock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension
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1 Brock Uniersiy Physics 1P21/1P91 Fall 2013 Dr. D Agosino Soluions for Tuorial 3: Chaper 2, Moion in One Dimension The goals of his uorial are: undersand posiion-ime graphs, elociy-ime graphs, and heir connecions pracice using he kinemaics equaions for moion in one dimension 1. Alice walks along a sraigh sidewalk. Her posiion-ime graph is gien below. x (a) Draw Alice s elociy-ime graph in he space proided aboe. [4 poins] Soluion: The soluion is shown aboe.
2 (b) Briefly describe Alice s moion in words for each of he four segmens of her moion, including: he direcion of her moion; he sign of her elociy; wheher Alice is speeding up or slowing down; her acceleraion. [8 poins] Soluion: In he firs segmen, Alice raels in he posiie direcion a a consan speed (zero acceleraion). In he second segmen, Alice raels in he posiie direcion a a consan speed (zero acceleraion), bu he speed is less han in he firs segmen. In he hird segmen, Alice is sopped in he same posiion, which means her speed is zero (as is her elociy). In he fourh segmen, Alice raels in he negaie direcion a a consan speed (zero acceleraion), a a speed ha is beween he speeds in he firs wo segmens. Wihin each segmen of he moion, he acceleraion is zero. Howeer, here mus be some acceleraion beween each segmen; ha is, a he corner poins of he posiion-ime graph. These corners make he graph unrealisic, as hey sugges ha he acceleraion beween segmens of moion is infinie; making he corners rounded would make he graph more realisic. We e lef hem as corners o simplify he analysis (sraigh lines are easier o analyze han cures), bu i s good o recognize ha such graphs are no physically realisic. 2. Basil walks along a sraigh sidewalk. His elociy-ime graph is gien below. (a) Draw Basil s posiion-ime graph in he space proided aboe. [3 poins] Soluion: The graph is shown below. Noice ha we e omied he horizonal axis in his posiion-ime graph. Saring from he elociy-ime graph, here is no way of knowing he alue of he Basil s iniial posiion, so here are an infinie number of alid posiion-ime graphs ha mach he gien elociy-ime graph, one for each of he placemens of he horizonal axis. (Calculus loers will recognize his as a manifesaion of he consan of inegraion ha resuls from ani-differeniaing he elociy funcion o obain he posiion funcion. Each alue of he consan of inegraion (which corresponds o he iniial posiion) corresponds o a differen placemen of he horizonal axis of he posiion-ime graph. Anoher way o say he same hing is ha differen choices of he consan of inegraion ranslae he posiion-ime graph erically.) (b) Briefly describe Basil s moion in words for each of he hree segmens of his moion, including: he direcion of his moion; he sign of his elociy; wheher Basil is speeding up or slowing down; his acceleraion. [6 poins] Soluion: In he firs segmen, Basil moes in he negaie direcion a a consan speed (zero acceleraion). In he second segmen, Basil is sopped, so his posiion is consan, his elociy and speed are zero, and his acceleraion is also zero. In he hird segmen, Basil moes in he posiie direcion, bu his elociy (and speed) decrease (so his acceleraion is negaie) unil he sops a he end of he hird segmen.
3 x 3. Clearly indicae wheher he following saemen is TRUE or FALSE. Then proide a brief explanaion, including a correcion if he saemen is incorrec. [2 poins] The objec is speeding up. x Soluion: FALSE. The slope of he graph is consan, which means ha he elociy is consan, which means ha he speed is consan. The posiion is increasing, no he speed.
4 4. Clearly indicae wheher he following saemen is TRUE or FALSE. Then proide a brief explanaion, including a correcion if he saemen is incorrec. [2 poins] The objec is speeding up. Soluion: TRUE. The ploed alues increase as ime passes, and he ploed alues represen he elociy. Because he objec is moing in he posiie direcion, he fac ha he elociy increases means ha he speed increases. Anoher way o see his is o noe ha he elociy is posiie and he acceleraion (he slope of his graph) is also posiie, so he speed increases. 5. Charles hrows a baseball sraigh down from he op of a ery high cliff wih an iniial speed of 26 m/s. (a) Deermine he baseball s speed afer (i) 1 s, (ii) 2 s, and (iii) 3 s. [3 poins] Soluion: I ll choose down as he posiie direcion; hen a = m/s 2. Now rearrange he equaion = a o obain = a f i = a f = i + a f = Le 1 represen he elociy of he baseball 1 s, le 2 represen he elociy of he baseball afer 2 s, and le 3 represen he elociy of he baseball afer 3 s. Then, using he equaion f = i + a, we obain (rounded o wo significan figures) 1 = (1) = 36 m/s 2 = (2) = 46 m/s 3 = (3) = 55 m/s The elociies are all posiie (i.e., direced downward), so he speeds are he same as he elociies in his case. Do hese resuls make sense? Remember ha for a freely falling objec, eery second he speed of he objec increases by 9.80 m/s 2.
5 (b) Deermine he baseball s posiion afer (i) 1 s, (ii) 2 s, and (iii) 3 s. [6 poins] Soluion: Le s use he op of he cliff as a reference poin, and label his posiion by x = 0. We ll choose down as he posiie direcion, as we did in Par (a). To deermine he posiions of he baseball a he gien imes, rearrange he following equaion: 2 f 2 i = 2a x Therefore, x = 2 f 2 i 2a x f x i = 2 f 2 i 2a x f 0 = 2 f (9.8) x f = 2 f 26 2 x 1 = x 2 = x 3 = = = = = 30 m = 72 m = 120 m Noe ha we e used alues of i wih more han wo significan figures in our calculaions o obain he posiions. This is a good habi, and will aoid rounding errors. In general, if your final resuls should be accurae o wo significan figures, use more han wo significan figures in he calculaions.
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