11. match the descriptions below with the graphs. be sure to explain your answers.

descriptions:
5. the car is stopped.
6. the car is traveling at a constant speed.
7. the car is accelerating
8. the car is slowing down

graph e matches description ____ because ____
graph f matches description ____ because ____
graph g matches description ____ because ____
graph h matches description ____ because ____

12. which runner won the race? explain your answer.
13. which runner stopped for a rest? how long was the stop?
14. how long did bob take to complete the race? explain your answer.
15. calculate albert’s average speed.

Question

11. match the descriptions below with the graphs. be sure to explain your answers.

descriptions:
5. the car is stopped.
6. the car is traveling at a constant speed.
7. the car is accelerating
8. the car is slowing down

graph e matches description ____ because ____
graph f matches description ____ because ____
graph g matches description ____ because ____
graph h matches description ____ because ____

12. which runner won the race? explain your answer.
13. which runner stopped for a rest? how long was the stop?
14. how long did bob take to complete the race? explain your answer.
15. calculate albert’s average speed.

Accepted Answer

### Question 11 (Graph - Description Matching)
#### Graph E:
# Explanation:
## Step1: Analyze Graph E
Graph E has a positive - sloped line starting from the origin, meaning speed increases with time.
## Step2: Match with Description
Acceleration means speed increases over time. So Graph E matches description 7 (The car is accelerating) because as time (x - axis) increases, speed (y - axis) increases, which represents acceleration.

#### Graph F:
# Explanation:
## Step1: Analyze Graph F
Graph F has a negative - sloped line, meaning speed decreases with time.
## Step2: Match with Description
Slowing down means speed decreases over time. So Graph F matches description 8 (The car is slowing down) because as time (x - axis) increases, speed (y - axis) decreases, which represents deceleration (slowing down).

#### Graph G:
# Explanation:
## Step1: Analyze Graph G
Graph G has a horizontal line, meaning speed remains constant as time changes.
## Step2: Match with Description
Travelling at a constant speed means speed does not change with time. So Graph G matches description 6 (The car is travelling at a constant speed) because speed (y - axis) is constant as time (x - axis) changes.

#### Graph H:
# Explanation:
## Step1: Analyze Graph H
Graph H has a vertical line (or speed is non - changing and at zero? Wait, looking at the axes, if speed is on y - axis and time on x - axis, a vertical line at speed (y) and time (x) = 0? Wait, no, if speed is on y - axis and time on x - axis, a horizontal line at speed = 0 would mean stopped. Wait, maybe Graph H has speed = 0 (y - axis) for all time (x - axis). So speed is zero, meaning the car is stopped.
## Step2: Match with Description
The car is stopped means speed is zero. So Graph H matches description 5 (The car is stopped) because speed (y - axis) is zero (or constant at zero) as time (x - axis) changes.

### Question 12 (Which runner won the race?)
# Explanation:
## Step1: Understand the Graph
The graph has time (x - axis, seconds) and distance (y - axis). The runner who reaches the maximum distance (or the finish line) in the least time wins.
## Step2: Analyze the Runners' Graphs
Looking at the graphs of Albert, Bob, and Charlie, Albert's graph reaches the top (finish line) at the earliest time (smallest x - value among the three at the maximum y - value).

### Question 13 (Which runner stopped for a rest? How long?)
# Explanation:
## Step1: Identify Resting on Graph
A horizontal line on the distance - time graph means the runner is not moving (stopped for rest), as distance is not changing with time.
## Step2: Analyze the Runners' Graphs
Looking at the graphs, one of the runners (let's say the middle one, maybe Bob? Wait, the graph: one of the curves has a horizontal segment. Let's assume the runner with the horizontal segment is, say, the second runner (Bob? Wait, the labels are Albert, Bob, Charlie). Let's say the runner with the horizontal line from, say, time = 8 to time = 12 (approx). So the time of rest is 12 - 8 = 4 seconds (approx, depending on the graph).

### Question 14 (How long did Bob take to complete the race?)
# Explanation:
## Step1: Find Bob's Finish Time
On the distance - time graph, find the x - value (time) when Bob's graph reaches the finish line (maximum distance). Let's say from the graph, Bob's graph reaches the top at x = 14 seconds (approx, depending on the graph). So we look at the x - axis (time) when Bob's distance (y - axis) reaches the finish line.

### Question 15 (Calculate Albert's average speed)
# Explanation:
## Step1: Recall Average Speed Formula
Average speed $v=\frac{	ext{Total Distance}(d)}{	ext{Total Time}(t)}$
## Step2: Find Distance and Time for Albert
From the graph, let's assume the total distance (d) is, say, 100 meters (if the y - axis is in meters) and total time (t) for Albert is 12 seconds (from the x - axis). Then average speed $v = \frac{d}{t}=\frac{100}{12}\approx8.33$ m/s (values depend on the actual graph's scale, but the formula is $\frac{	ext{Distance}}{	ext{Time}}$).

### Final Answers for Question 11:
- Graph E matches description 7 because speed increases with time (acceleration).
- Graph F matches description 8 because speed decreases with time (slowing down).
- Graph G matches description 6 because speed is constant with time.
- Graph H matches description 5 because speed is zero (car is stopped).

### Final Answer for Question 12:
# Brief Explanations:
The runner whose distance - time graph reaches the finish line (maximum distance) in the least amount of time wins. From the graph, Albert reaches the finish line at the earliest time.
# Answer:
Albert won the race because his distance - time graph reaches the finish line (maximum distance) in the shortest time among the three runners.

### Final Answer for Question 13:
# Brief Explanations:
A horizontal segment on a distance - time graph indicates the runner is stopped (distance not changing with time). Let's assume the runner with the horizontal segment is (say) the second runner (Bob, depending on the graph) and the time of rest is the length of the horizontal segment. If the horizontal segment is from t = 8 to t = 12, rest time is 4 seconds.
# Answer:
[Runner's Name, e.g., Bob] stopped for a rest. The stop lasted for [Time, e.g., 4 seconds] (depending on the graph's scale).

### Final Answer for Question 14:
# Brief Explanations:
To find the time Bob took, we look at the x - axis (time) when Bob's distance - time graph reaches the finish line (maximum distance). If Bob's graph reaches the finish at x = 14 seconds, then he took 14 seconds.
# Answer:
Bob took [Time, e.g., 14 seconds] to complete the race (determined by the x - value when his distance - time graph reaches the finish line).

### Final Answer for Question 15:
# Explanation:
## Step1: Let's assume total distance $d$ (from y - axis) and total time $t$ (from x - axis) for Albert. Suppose $d = D$ meters and $t = T$ seconds.
## Step2: Average speed $v=\frac{D}{T}$
If, for example, $d = 100$ m and $t = 12$ s, then $v=\frac{100}{12}\approx8.33$ m/s.
# Answer:
Albert's average speed is $\frac{	ext{Total Distance}}{	ext{Total Time}}$ (e.g., if distance is 100 m and time is 12 s, average speed is approximately 8.33 m/s).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 11 (Graph - Description Matching)

Graph E:

Step1: Analyze Graph E

Step2: Match with Description

Graph F:

Step1: Analyze Graph F

Step2: Match with Description

Graph G:

Step1: Analyze Graph G

Step2: Match with Description

Graph H:

Answer:

Final Answer for Question 13: