To determine which statement does NOT describe the cart's motion based on the graph, we can analyze each statement in relation to the Distance vs. Time graph provided:
A. The cart moved 24 m away from the starting point between 2 s and 5 s.
B. The cart moved toward the starting point at a speed of 3 m/s between 7 s and 12 s.
C. The cart moved 11 m toward the starting point between 8 s and 10 s.
D. The cart moved away from the starting point at a speed of 1 m/s for 2 s.
Let's analyze each statement:
A. Between 2 s and 5 s, the cart's distance increases from 5 m to its maximum at 25 m. The change in distance is \( 25 m - 5 m = 20 m \), not 24 m. So this statement is a possible incorrect description.
B. There is no data shown for the time interval between 7 s and 12 s, so we cannot confirm or refute this statement directly from the graph. However, given that the graph ends at 10 s, this statement might imply a continuation beyond the graph, which we cannot verify. Thus, this statement is potentially incorrect because it references a time beyond the provided graph.
C. Between 8 s and 10 s, the cart's distance decreases from 25 m back to 15 m. The change in distance is \( 25 m - 15 m = 10 m \), not 11 m. Therefore, this statement could also be incorrect.
D. To assess speed, we look at the slope of the graph. A slope of 1 m/s would mean that for every second that passes, the cart moves 1 m. The graph does not show a constant slope of 1 m/s for any 2-second interval, so this statement might not accurately describe the motion shown.
Let's perform calculations for each statement based on the graph to find which one does NOT describe the cart's motion. We will calculate the actual distances and speeds in the given time intervals.
For statement A:
- At 2 s, the distance is 5 m.
- At 5 s, the distance is at its maximum of 25 m.
- The difference in distance is \( 25 m - 5 m = 20 m \).
For statement C:
- At 8 s, the distance is 25 m.
- At 10 s, the distance is 15 m.
- The difference in distance is \( 25 m - 15 m = 10 m \).
Statement D does not require calculation because the graph shows that the cart's speed is not 1 m/s for any 2-second interval.
Since statement B refers to a time interval not shown on the graph, it cannot be directly refuted by the graph. However, by process of elimination, if we assume that the graph provided all the necessary information, statement B would not be correct because it refers to data not present on the graph. However, it is important to note that without data beyond 10 seconds, we cannot conclusively determine the correctness of statement B.
Let's confirm statements A and C with calculations and then discuss which of them, including B and D, is most likely to be incorrect.
The calculations confirm that:
- For statement A, the change in distance between 2 seconds and 5 seconds is \( 20 \) meters, not \( 24 \) meters as stated.
- For statement C, the cart moved \( 10 \) meters toward the starting point between 8 seconds and 10 seconds, not \( 11 \) meters as stated.
Given that both statements A and C contain discrepancies, and without further information, we cannot conclusively determine which one does NOT describe the cart's motion solely based on the graph.
However, statement D describes a consistent speed of 1 m/s for 2 seconds, which is not depicted anywhere on the graph, making it likely incorrect. Furthermore, statement B mentions a time interval not shown on the graph (between 7 s and 12 s), making it impossible to verify based on the provided information.
If we must choose which statement does NOT describe the cart's motion based on the given graph, statement B is technically correct because it cannot be evaluated with the provided information, and statement D is incorrect because the graph does not show a consistent speed of 1 m/s for any 2-second interval. Therefore, statement D is the most likely answer since it describes a motion that is not supported by the graph, whereas statement B refers to a time outside of the graph's scope.