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13 Nov 2019
Problem 1. Sophie's cat Cale is chasing a red dot along a wall. The wall is 24 feet long., and when the game starts, Cale is on the left end of the wal and the red dot is in the center Letjt) and ( be Cale's and the red dot's velocity, respectively, in feet per second, t seconds into the game, where a positive velocity means movement to the right, and a negative velocity means movement to the left. Below is a graph showing both j(t) (solid ine, i blue) and ( (dotted, in red) for the first 24 seconds of the game. o-o 16 18 2 2 24 -3 ustify all gour answers. (a) Over what intervals of time is Cale moving to the right? (b) At what time(s) is Cale's velocity greatest? (c) At what time(s) is Cale furthest to the right? (d) At what time(s) are Cale and the red dot moving at the same velocity? (e) How many times are Cale and the red dot in the same location during these 24 seconds? (f) How far, in tota, has Cale traveled in these 24 seconds? Express your answer as an integral and provide an exact value. (g) How far from the left end of the wall is Calc after 24 seconds? Express your answer as an integral and provide an exact value. (h) After 22 seconds, Calc stays where it is while the red dot continues to move at a constant velocity. At what time are Cakc and the red dot in the same location along the wall?
Problem 1. Sophie's cat Cale is chasing a red dot along a wall. The wall is 24 feet long., and when the game starts, Cale is on the left end of the wal and the red dot is in the center Letjt) and ( be Cale's and the red dot's velocity, respectively, in feet per second, t seconds into the game, where a positive velocity means movement to the right, and a negative velocity means movement to the left. Below is a graph showing both j(t) (solid ine, i blue) and ( (dotted, in red) for the first 24 seconds of the game. o-o 16 18 2 2 24 -3 ustify all gour answers. (a) Over what intervals of time is Cale moving to the right? (b) At what time(s) is Cale's velocity greatest? (c) At what time(s) is Cale furthest to the right? (d) At what time(s) are Cale and the red dot moving at the same velocity? (e) How many times are Cale and the red dot in the same location during these 24 seconds? (f) How far, in tota, has Cale traveled in these 24 seconds? Express your answer as an integral and provide an exact value. (g) How far from the left end of the wall is Calc after 24 seconds? Express your answer as an integral and provide an exact value. (h) After 22 seconds, Calc stays where it is while the red dot continues to move at a constant velocity. At what time are Cakc and the red dot in the same location along the wall?
Lelia LubowitzLv2
28 Feb 2019