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Question

Lisa was trying to park her car. She moved her car forward at a constant velocity for 5 seconds, and then backward at a constant velocity for 10 seconds. She then moved her car forward again at a constant velocity for the next 5 seconds, and then she stopped. Which of the following graphs could represent the motion of Lisa's car?

    

Answer 1

Hello Keef 6,

To understand what this question is asking you need a bit of intuition, the question describes Lisa's movement in plain English but the answers are defined in terms of points on a graph. The best way to understand how to solve this question is to graph out all four answers and then compare them to the description of Lisa's motion.

Click the following link to see Solution A visualized as a graph (using the website Wolfram Alpha):

https://www.wolframalpha.com/input/?i=graph+points+(0,0);+(5,20);+(15,10);+(20,40);+(50;0)

Using intuition, the X component of all of these points represent the time of Lisa's motion, i.e. between (0,0) and (5,20) Lisa drove forward for 5 seconds. The second point goes from X=5 to X=15, Lisa drives back for 15 - 5 = 10 seconds. It becomes clear that X represents total duration of travel. The Y component of all of these points appears to represent distance: Lisa drove forward 20 feet from 0 to 5 seconds, then from 5 seconds to 15 seconds she drove 10 - 20 = -10 feet (i.e. backwards 10 feet). It becomes clear that Y is overall distance from the origin. You now know that X = total duration and Y = total distance, now that you understand what these graphs represent simply plot them all and apply logic to see which fits best.

Here is the logic you would use to confirm or disconfirm the possible solutions:

Solution A states that the fourth line joins (20,40) and (50,0), which means Lisa drove backwards 40 feet in 30 seconds. This is incorrect as Lisa stopped moving based on the description.

Solution B states that the second line joins (5,20) and (15,30), which means Lisa drove forward 10 feet in 10 seconds. This is incorrect as Lisa drove backwards at a constant velocity based on the description.

Solution C states that the second line joins (5,40) and (15,45), which means Lisa drove forward 5 feet in 10 seconds. This is incorrect as Lisa drove backwards at a constant velocity based on the description.

Solution D is similar to Solution A, except the fourth straight line joins (20,40) and (50,40). If you graph these two points it shows a straight line over a period of 30 seconds, meaning Lisa stopped moving during this time. This is accurate based on the description, therefore this is the correct answer.