AP QUIZ # GRAPHING MOTION ) POSITION TIME GRAPHS DISPLAEMENT Ech grph below shows the position of n object s function of time. A, B,, D, Rnk these grphs on the gretest mgnitude displcement during the time interl from to. Gretest Explin your resoning.,,, 3 Lest, Answer: > B > A = D. The displcement is gien by the chnge in position oer the time interl. Object hs displcement with mgnitude of m; B s displcement hs mgnitude of m nd A nd D both he displcements since they re t the sme point t the strt nd end of the time interl. the sme nnot ) Grphs Aerge Speed Ech grph below shows the position of n object s function of time. A, B,, D,,,,, Rnk these grphs on the erge speed of the object during the time interl from to. Gretest 3 Lest Explin your resoning. Answer: D > > B > A. The erge speed is the distnce treled diided by the time interl. For D, the erge speed is m/s (the object treled in one direction nd then bck for totl of in ); for it is m/s; for B it is m/s; nd for A it is. the sme nnot 3) VELOITY VS. TIME GRAPH I AELERATION VS. TIME GRAPH A student obtins grph of n object s elocity ersus time nd then drws the grph of the ccelertion ersus time for the sme time interl. Wht, if nything, is wrong with the grph of the ccelertion ersus time? If something is wrong, identify it nd explin how to correct it. If the grph is correct, explin why.
Answer: The ccelertion is the slope of the elocity grph. Thus, the third nd fourth peks should be reersed s shown below becuse the sign of the ccelertion is the sme s the sign of the slope of the elocity-time grph. ) VELOITY VS. TIME GRAPHS DISPLAEMENT The grphs represent the elocity of two toy robots moing in one dimension for prticulr time interl. Both grphs he the sme time nd elocity scles. se A se B Is the mgnitude of the displcement of the robot for the entire time interl shown () greter in cse A, (b) greter in cse B, or (c) the sme in both cses? Explin your resoning. Answer: The displcement is the re between the elocity-time line, or cure, nd the time xis. The displcement in se A is (there is negtie displcement for the first hlf nd n equl mgnitude positie displcement for the second hlf) while the displcement for cse B is negtie. The mgnitude of the displcement is (b) greter in cse B. 5) AELERATION VS. TIME GRAPH I VELOITY VS. TIME GRAPH A student obtins grph of n object s ccelertion ersus time nd then drws the grph of the elocity ersus time for the sme time interl. The object strts from rest. Wht, if nything, is wrong with the grph of elocity ersus time? If something is wrong, identify it nd explin how to correct it. If the grph is correct, explin why. Answer-the chnge in elocity is relted to the re under the ccelertion s time grph. Thus the elocity grph should be like the grph below. The second, third nd fourth ccelertions re ll the sme mgnitude nd re smller thn the initil ccelertion, so the elocity does not return to t the end of the interl.
) VELOITY VS. TIME GRAPH I AELERATION VS. TIME GRAPH A student obtins grph of n object s elocity ersus time nd then drws the grph of the ccelertion ersus time for the sme time interl. Wht, if nything, is wrong with the grph of the ccelertion ersus time? If something is wrong, identify it nd explin how to correct it. If the grph is correct, explin why. Answer: Since the ccelertion-time grph is relted to the slope of the elocity-time grph, the mgnitude of the ccelertion should be proportionl to the slope of the elocity-time grph t ech point. For the third segment of the elocity-time grph, the (positie) slope hs greter mgnitude thn the (negtie) slope of the first segment, nd so the ccelertion should he greter positie lue for this segment thn the negtie lue of the first segment. (The chnge in elocity for the object oer the entire time interl is, so the re under the cure of the ccelertion time grph should be. We need to djust the ccelertion grph to bring the elocity bck to the originl lue, nd the rectngles boe nd below the xis should he the sme re. 7) AELERATION VS. TIME GRAPH II VELOITY VS. TIME GRAPH Sketch possible elocity ersus time grph gien the ccelertion grph for the sme time interl. Explin. Answer: The chnge in the elocity is relted to the re under the ccelertion grph. The second blip is tller thn the first so it contins more re. onsequently it represents greter chnge in elocity. Since there is no prticulr initil elocity gien, ny grph of the sme shpe but strting t some other initil elocity would lso be correct choice.
) VELOITY VS. TIME GRAPHS OF TWO OBJETS II DISPLAEMENT The grphs below show the elocity of two objects during the sme time interl. Object, Object, For the -second time interl shown, is the displcement of Object in the upper grph () greter thn, (b) equl to, or (c) less thn the displcement of Object in the lower grph? Explin. Answer: The displcement is greter for Object since the displcement is equl to the re under the line or cure representing the motion in grph of elocity s. time. 9) VELOITY VS. TIME GRAPHS DISPLAEMENT Shown below re six elocity-time grphs for toy robots tht re treling long stright hllwy. grphs he the sme time nd elocity scles. A B D E F Rnk these situtions on the mgnitudes of the displcements during these interls. Gretest 3 5 Lest the sme nnot Explin your resoning. Answer: D > A > B = > F > E; since these re elocity ersus time grphs the displcements re gien by the res under (between the lines nd the time xis) the lines in the grphs.
) BALL THROWN UPWARD AND OMES BAK DOWN V VS. T GRAPH, m/s A bll is thrown stright upwrd nd flls bck to the sme height. A student mkes this grph of the elocity of the bll s function of time. Wht, if nything, is wrong with the student s grph? If something is wrong, explin the error nd how to correct it. If the grph is correct, explin why., s, m/s, s ) VELOITY VS. TIME GRAPHS DISTANE TRAVELED -time grphs for six toy robots tht re treling long stright hllwy re shown. grphs he the sme time nd elocity scles. A B D E F Rnk these situtions on the distnce treled during these interls. Gretest 3 5 Lest the sme nnot Explin your resoning. Answer: D > A > B = > E = F. The distnce treled is the sum of the bsolute lues of the res between the horizontl xis nd the line on ech grph. For grphs of motion tht don t chnge direction (ll cses except E), the mgnitude of the displcement is the sme s the distnce treled. For cse, E, the distnce treled is the sum of the distnce treled bckwrd nd the distnce treled forwrd. The bsolute lue of the two res in cse E is the sme s the re in cse F. ) POSITION VS. TIME GRAPHS AELERATION AND VELOITY ersus time grphs for bots treling long nrrow chnnel re shown below. The scles on both xes re the sme for ll of these grphs. In ech grph, point is mrked with dot.
A B D E F G H I ) For which of these cses, if ny, is the position t the indicted point? Answer: The position is for the indicted point in grph, which cn be red directly off of the grph. b) For which of these cses, if ny, is the position negtie t the indicted point? Answer: The position is for cse, positie for E, G, nd I, nd negtie for A, B, D, F, H. c) For which of these cses, if ny, is the elocity t the indicted point? Answer: The elocity is if the slope of the grph is t the indicted point, which is the cse only for grph E. d) For which of these cses, if ny, is the elocity negtie t the indicted point? Answer: The elocity is gien by the slope of the position-time grph, nd negtie elocity corresponds to downwrd-sloping grph t the indicted point. Grphs D, F, G, nd I he negtie slopes t the indicted point. e) For which of these cses, if ny, is the ccelertion t the indicted point? Answer: A ccelertion corresponds to constnt elocity, which in turn corresponds to liner positiontime grph. The ccelertion is for grph A. f) For which of these cses, if ny, is the ccelertion negtie t the indicted point? A negtie ccelertion corresponds to elocity grph whose slope is negtie, which in turn corresponds to position-time grph tht cures downwrd (i.e., the slope becomes less positie or more negtie with time. The ccelertions re negtie for grphs, E, F, nd H.