A college student named Nova walked 500 meters for 500 seconds from her dormitory building to find her favorite bench in a park. She called her mom and talked for 100 seconds at the bench, but suddenly she remembered that she
did not turn off the gas stove. So, she returned her dorm by running for 100 seconds. To find out Nova's average
velocity for each case while walking, resting, and running, begin by plotting a graph between position and time. Please
be aware that the walking mode is a positive direction and the running mode is a negative direction of Nova's motion.
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Unit I Di:
Complete the Graph: The graph below will show you Nova's distance from her dormitory building at a given time.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

answercollision;

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