Section 6.5 - Describing Situations From Graphs

1.

Which shows a non-linear relationship?

Graph A

Graph B

Graph C

Graph D

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

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.

2.

A rocket is shot into the air. This table shows the height of the rockets after various time intervals. When does the rockets reach its maximum height?

1.2s

2.0s

2.4s

7.2s

The rocket reaches its maximum height at 1.2s.

Explanation

The rocket reaches its maximum height at 1.2s.

3.

Which graph shows a negative velocity?

Graph A

Graph B

Graph C

Graph D

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

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.

4.

Which story matches the graph?

Olivia throws a rock off a cliff into the ocean below

Francine hits a home run

A hang glider flies off a cliff, does one full turn and lands where he began

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

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.

5.

This graph shows how a kayak travels over time. Over what interval is the kayak travelling the slowest?

0s - 20s

20s - 40s

60s - 80s

80s - 100s

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.

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.

6.

What is the slope of the graph between 50s and 60s

1/10

1/2

2

5

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

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.

7.

Susan drove to the shopping centre, stopping at 2 lights along the way. After shopping, she retured home, driving at a steady rate. Which graph matches the situation?

Graph A

Graph B

Graph C

Graph D

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 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.

8.

If you fill the pitcher with water, pouring at a steady rate, in which section will it fill the fastest?

Section 1

Section 2

Section 3

Section 4

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

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.

9.

Ben walks tp the bus stop. The he realizes he has forgotten his lunch and runs back home. The he runs back to the bus stop. Which graph best describes the story?

Graph A

Graph B

Graph C

Graph D

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

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.

10.

This graph shows how mountain bike travels over time. At what interval of time is the mountain bike travelling the fastest?

0s - 10s

20 s - 30 s

30s - 50 s

50s - 60s

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

Explanation

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