Question
Question 10 (1 point)
Alyssa did an experiment to study the motion of a moving object. First, she collected measurements of the total distance the object traveled at various times after the moment at which she began her observation. Then, she prepared a graph to plot the data she collected. The first data point that Alyssa recorded was at (2, 20), as shown in the graph below.
Image
Assuming that the speed of the object that Alyssa observed was constant, which data point should Alyssa correctly plot next on her graph?
a
(6, 50)
b
(5, 30)
c
(4, 40)
d
(3, 40)
Alyssa did an experiment to study the motion of a moving object. First, she collected measurements of the total distance the object traveled at various times after the moment at which she began her observation. Then, she prepared a graph to plot the data she collected. The first data point that Alyssa recorded was at (2, 20), as shown in the graph below.
Image
Assuming that the speed of the object that Alyssa observed was constant, which data point should Alyssa correctly plot next on her graph?
a
(6, 50)
b
(5, 30)
c
(4, 40)
d
(3, 40)
Answers
GPT-4o mini
To determine which data point Alyssa should correctly plot next based on the first data point (2, 20), we need to use the formula for constant speed, which is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
From the first data point (2, 20), we can see that at time \( t = 2 \) seconds, the object has traveled a distance of \( d = 20 \) units.
Since the speed is constant, we need to consider the ratio of distance to time. If we plot again, we will look for a point where the distance increases proportionately according to the time.
Here's how we can analyze the options:
1. **Option a: (6, 50)**
- Time = 6, Distance = 50
- Speed = \( \frac{50}{6} = \approx 8.33 \)
2. **Option b: (5, 30)**
- Time = 5, Distance = 30
- Speed = \( \frac{30}{5} = 6 \)
3. **Option c: (4, 40)**
- Time = 4, Distance = 40
- Speed = \( \frac{40}{4} = 10 \)
4. **Option d: (3, 40)**
- Time = 3, Distance = 40
- Speed = \( \frac{40}{3} \approx 13.33 \)
Looking at the first data point (2, 20) and comparing the ratios or the amount of distance traveled:
- From \( t = 2 \) to \( t = 3 \), the distance should increase.
- From \( t = 2 \) to \( t = 3\), the distance must increase by a constant amount as per constant speed.
Since the distance at (2, 20) is 20, the next appropriate point that aligns with consistent increases of distance would be the one where \( t = 3 \).
To find out the correct next data point that allows constant speed:
From (2, 20) to (3, 30) should continue the linear pattern. None of the options hold the data point of (3, 30).
Hence,
Comparing distances at given times:
- At \( t = 3 \), the distance at 40 would match the increasing proportion pattern set by the first point.
Thus, the answer is:
**c - (4, 40)**
This set pattern keeps the speed relatively constant at each step, allowing Alyssa to have an accurate representation of the object's motion.
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
From the first data point (2, 20), we can see that at time \( t = 2 \) seconds, the object has traveled a distance of \( d = 20 \) units.
Since the speed is constant, we need to consider the ratio of distance to time. If we plot again, we will look for a point where the distance increases proportionately according to the time.
Here's how we can analyze the options:
1. **Option a: (6, 50)**
- Time = 6, Distance = 50
- Speed = \( \frac{50}{6} = \approx 8.33 \)
2. **Option b: (5, 30)**
- Time = 5, Distance = 30
- Speed = \( \frac{30}{5} = 6 \)
3. **Option c: (4, 40)**
- Time = 4, Distance = 40
- Speed = \( \frac{40}{4} = 10 \)
4. **Option d: (3, 40)**
- Time = 3, Distance = 40
- Speed = \( \frac{40}{3} \approx 13.33 \)
Looking at the first data point (2, 20) and comparing the ratios or the amount of distance traveled:
- From \( t = 2 \) to \( t = 3 \), the distance should increase.
- From \( t = 2 \) to \( t = 3\), the distance must increase by a constant amount as per constant speed.
Since the distance at (2, 20) is 20, the next appropriate point that aligns with consistent increases of distance would be the one where \( t = 3 \).
To find out the correct next data point that allows constant speed:
From (2, 20) to (3, 30) should continue the linear pattern. None of the options hold the data point of (3, 30).
Hence,
Comparing distances at given times:
- At \( t = 3 \), the distance at 40 would match the increasing proportion pattern set by the first point.
Thus, the answer is:
**c - (4, 40)**
This set pattern keeps the speed relatively constant at each step, allowing Alyssa to have an accurate representation of the object's motion.