Question

A marble is placed on a number line. Its position away from the origin after a given time is shown in the graph below.





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On the graph, positive positions indicate positions to the right of the origin and negative positions indicate positions to the left of the origin. Which statement is true?


The marble remains stationary for a total of 3 seconds.


The marble is located to the left of the origin for 3 seconds.


The marble begins its motion at a position of 50 feet to the left of the origin.


The average rate of change of the marble's position relative to the origin is greatest between 10 seconds and 12 seconds.

Answer 1

I can’t see the graph you referenced — could you either upload it or describe the key points (positions at the labeled times and any flat/horizontal segments)?

To help you check each statement, here’s how to read the graph:

- “Remains stationary for a total of 3 seconds.”
Look for horizontal segments (slope = 0). Add the durations of all horizontal segments. If their total length equals 3 s, the statement is true.

- “Is located to the left of the origin for 3 seconds.”
Count the total time during which the position (vertical value) is negative (below the horizontal axis). If that total is 3 s, the statement is true.

- “Begins its motion at a position of 50 feet to the left of the origin.”
Check the vertical value at time t = 0. If it is −50 ft, this is true.

- “The average rate of change of the marble's position relative to the origin is greatest between 10 seconds and 12 seconds.”
Compute the average rate of change (slope) on each interval of interest: (position at end − position at start)/(time interval). Compare absolute values (largest magnitude = greatest speed). If the slope between 10 and 12 s has the largest magnitude, the statement is true.

If you upload the graph or tell me the coordinates/values at the key times and where the graph is flat/negative, I’ll compute and tell you which statement is true.