activity b (continued from previous page)
5. with number of points set to 3, create the graph shown at right. your graph should include (0, 0), (2, 10), and (4, 40).
a. where does the runner start? ______
b. where will he be after 2 seconds? ______
c. where will he be after 4 seconds? ______
d. in which time interval do you think the runner will be moving most quickly? (circle your answer below.)
0 to 2 seconds 2 to 4 seconds
6. click the start button and watch the animation. what about the runner changed after 2 seconds of running? ______
______
7. speed is a measure of how fast something is moving. to calculate speed, divide the distance by the time. in the gizmo, the units of speed are yards per second (y/s).
a. in the first 2 seconds, how far did the runner go? ______
b. in this time interval, how far did the runner go each second? ______
c. in this time interval, what was the runner’s speed? ______
8. now look at the last two seconds represented on the graph.
a. in the last 2 seconds, how far did the runner go? ______
b. in this time interval, how far did the runner go each second? ______
c. in this time interval, what was the runner’s speed? ______
9. click the reset button. experiment with a variety of graphs, focusing on the speed of the runner. in general, how can you estimate the speed of the runner by looking at a graph?
______
______
______

Question

activity b (continued from previous page)
5. with number of points set to 3, create the graph shown at right. your graph should include (0, 0), (2, 10), and (4, 40).
   a. where does the runner start? ______
   b. where will he be after 2 seconds? ______
   c. where will he be after 4 seconds? ______
   d. in which time interval do you think the runner will be moving most quickly? (circle your answer below.)
      0 to 2 seconds        2 to 4 seconds
6. click the start button and watch the animation. what about the runner changed after 2 seconds of running? ______
   ______
7. speed is a measure of how fast something is moving. to calculate speed, divide the distance by the time. in the gizmo, the units of speed are yards per second (y/s).
   a. in the first 2 seconds, how far did the runner go? ______
   b. in this time interval, how far did the runner go each second? ______
   c. in this time interval, what was the runner’s speed? ______
8. now look at the last two seconds represented on the graph.
   a. in the last 2 seconds, how far did the runner go? ______
   b. in this time interval, how far did the runner go each second? ______
   c. in this time interval, what was the runner’s speed? ______
9. click the reset button. experiment with a variety of graphs, focusing on the speed of the runner. in general, how can you estimate the speed of the runner by looking at a graph?
   ______
   ______
   ______

Accepted Answer

### Question 5 (parts A - D)
#### 5A
# Brief Explanations:
The graph includes the point (0, 0). In a distance - time graph, the x - axis is time and the y - axis is distance. At time $t = 0$ seconds, the distance is 0 yards. So the runner starts at 0 yards (or the origin).
# Answer:
The runner starts at 0 yards (or the origin, represented by the point (0, 0)).

#### 5B
# Brief Explanations:
The graph has the point (2, 10). This means at $t=2$ seconds, the distance covered by the runner is 10 yards.
# Answer:
After 2 seconds, the runner will be at 10 yards.

#### 5C
# Brief Explanations:
The graph has the point (4, 40). So at $t = 4$ seconds, the distance covered by the runner is 40 yards.
# Answer:
After 4 seconds, the runner will be at 40 yards.

#### 5D
# Brief Explanations:
To find the speed in each interval, we use the formula $speed=\frac{distance}{time}$. For the interval 0 - 2 seconds: $speed_1=\frac{10 - 0}{2-0}=\frac{10}{2} = 5$ y/s. For the interval 2 - 4 seconds: $speed_2=\frac{40 - 10}{4 - 2}=\frac{30}{2}=15$ y/s. Since $15>5$, the runner is moving most quickly in the 2 to 4 seconds interval.
# Answer:
2 to 4 seconds

### Question 6
# Brief Explanations:
From the speed calculations in question 5, the speed of the runner changes from 5 y/s (in 0 - 2 seconds) to 15 y/s (in 2 - 4 seconds). So the runner's speed (or the rate of covering distance) increased after 2 seconds of running.
# Answer:
The runner's speed (the rate at which the runner covers distance) increased after 2 seconds of running.

### Question 7
#### 7A
# Brief Explanations:
Looking at the point (2, 10) on the graph, in the first 2 seconds (from $t = 0$ to $t=2$), the distance covered is $10 - 0=10$ yards.
# Answer:
In the first 2 seconds, the runner went 10 yards.

#### 7B
# Brief Explanations:
The total distance in 2 seconds is 10 yards. To find the distance per second, we divide the total distance by the total time. So $\frac{10}{2}=5$ yards per second.
# Answer:
In this time interval, the runner went 5 yards each second.

#### 7C
# Brief Explanations:
Using the formula $speed=\frac{distance}{time}$, with distance = 10 yards and time = 2 seconds, $speed=\frac{10}{2} = 5$ y/s.
# Answer:
In this time interval, the runner's speed was 5 yards per second (5 y/s).

### Question 8
#### 8A
# Brief Explanations:
At $t = 2$ seconds, the distance is 10 yards and at $t=4$ seconds, the distance is 40 yards. So the distance covered in the last 2 seconds (2 - 4 seconds) is $40 - 10 = 30$ yards.
# Answer:
In the last 2 seconds, the runner went 30 yards.

#### 8B
# Brief Explanations:
The total distance in 2 seconds (2 - 4 seconds) is 30 yards. To find the distance per second, we divide the total distance by the total time. So $\frac{30}{2}=15$ yards per second.
# Answer:
In this time interval, the runner went 15 yards each second.

#### 8C
# Brief Explanations:
Using the formula $speed=\frac{distance}{time}$, with distance = 30 yards and time = 2 seconds, $speed=\frac{30}{2}=15$ y/s.
# Answer:
In this time interval, the runner's speed was 15 yards per second (15 y/s).

### Question 9
# Brief Explanations:
In a distance - time graph, the slope of the line (or the line segment in a piece - wise graph) is given by the formula $slope=\frac{\Delta y}{\Delta x}=\frac{change\ in\ distance}{change\ in\ time}$, and since $speed = \frac{distance}{time}$, the slope of the distance - time graph represents the speed of the runner. A steeper slope means a higher speed, and a less - steep slope means a lower speed. So we can estimate the speed of the runner by looking at the slope of the graph (the steeper the graph, the faster the runner; the less steep, the slower the runner).
# Answer:
To estimate the speed of the runner from a distance - time graph, we look at the slope of the graph. The slope of the graph is calculated as $\frac{change\ in\ distance}{change\ in\ time}$, and since $speed=\frac{distance}{time}$, the slope of the distance - time graph represents the speed of the runner. A steeper slope indicates a higher speed, and a less steep slope indicates a lower speed.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 5 (parts A - D)

5A

Answer:

5B