Section 6.5 - Describing Situations From Graphs

Explanation
The graph shows a steady increase in speed followed by a sudden stop. This matches the action of Olivia throwing a rock off a cliff into the ocean below. The car pulling onto the highway and traveling at a steady speed does not match the sudden stop shown in the graph. Francine hitting a home run and the hang glider flying off a cliff and landing where he began do not match the steady increase in speed shown in the graph.

Explanation
Graph D shows a non-linear relationship because the points on the graph do not follow a straight line. Instead, they form a curve or a pattern that is not linear. This indicates that there is a relationship between the variables being plotted on the graph, but it is not a simple, direct relationship.

Explanation
The mountain bike is traveling the fastest during the interval of 0s - 10s.

Explanation
The slope of a graph represents the rate of change of the dependent variable with respect to the independent variable. In this case, the graph is being analyzed between the time intervals of 50s and 60s. The slope is determined by calculating the change in the dependent variable divided by the change in the independent variable. Since the graph does not provide specific values, it is not possible to calculate the exact slope. However, based on the given options, the correct answer is 1/2. This suggests that for every 1 unit increase in the independent variable (time), the dependent variable increases by a rate of 1/2.

Explanation
Graph C matches the situation because it shows Susan driving to the shopping center, stopping at 2 lights along the way, and then returning home at a steady rate. The graph accurately represents the scenario described in the question.

Explanation
Graph D shows a negative velocity because the line on the graph is sloping downwards from left to right. In physics, velocity is a vector quantity that refers to the rate at which an object changes its position. A negative velocity indicates that the object is moving in the opposite direction of the chosen positive direction. Therefore, the downward slope of the line in Graph D represents a negative velocity.

Explanation
Section 4 will fill the fastest because it has the largest volume compared to the other sections. As the pitcher is being filled at a steady rate, the section with the most volume will fill up more quickly than the others.

Explanation
The rocket reaches its maximum height at 1.2s.

Explanation
Graph C best describes the story because it shows Ben walking to the bus stop, then realizing he forgot his lunch and running back home, and finally running back to the bus stop. This sequence of events matches the actions described in the question.

Explanation
The kayak is traveling the slowest during the interval of 20s - 40s. This can be determined by observing the graph and identifying the section where the slope of the line representing the kayak's position is the least steep. In this interval, the kayak's position is changing at a slower rate compared to the other intervals, indicating slower travel speed.