Type your response in the box. imagine that you’re conducting a scientific observation of motion and will write a report describing the motion of the runner.
How would you describe the runner’s motion?
What information would help you accurately describe the motion?
What kind of drawing could you use to communicate your observation to someone else? Assume that you would want the person to look at your drawing and have a good idea of the runner’s movement.
In describing the motion of the runner, I would first mention key characteristics such as the direction, speed, and acceleration (if applicable) of the runner. I would describe if the runner's motion is uniform (constant velocity) or non-uniform (changing velocity). Additionally, I would note any significant changes in the runner's position, such as turning, stopping, or starting.
To accurately describe the motion, I would require information such as the distance covered by the runner, the time taken, the starting and ending positions, and any specific events or actions during the observation. Ideally, data like the runner's stride length, step frequency, or heart rate could provide more detailed insights into their motion.
To communicate my observation effectively, I would use a motion diagram or a series of sequential drawings. A motion diagram represents the position of the runner at specific time intervals, helping to visualize their trajectory. Alternatively, a series of simple stick-figure drawings with arrows indicating the direction of movement can also effectively convey the runner's motion. In both cases, including labels or captions with key details would further enhance understanding.
In this activity, you will choose appropriate scales and intervals for a piecewise linear relationship in the real world and create a graph of the relationship.
In the Warm-Up, you observed and described the motion of a runner. Watch the video again, and then answer the questions that follow.
Part A
Suppose you’re going to graph the relationship between distance (from starting position) and time in the video. Why is it unnecessary to show the graph below the horizontal axis or to the left of the vertical axis?
It is unnecessary to show the graph below the horizontal axis or to the left of the vertical axis because in the context of this video, distance and time are both positive quantities. The runner is moving forward, so the distance from the starting position is always increasing. Time is also always positive and progressing forward. Therefore, representing the relationship between distance and time only requires the graph to be shown in the positive quadrants of the coordinate plane.
What units would be appropriate for labeling the distance and time axes on the graph of this video?
For labeling the distance axis on the graph, appropriate units could be meters or kilometers, depending on the scale of the motion observed in the video. If the video focuses on short distances, meters may be more appropriate. However, if the runner covers larger distances, kilometers could be used.
On the time axis, appropriate units could be seconds or minutes, depending on the duration of the video and the time scale of the runner's motion. If the video captures a short span of time, seconds would work well. On the other hand, if the video covers a longer time period, minutes could be more suitable.
Would it be appropriate to label the time axis to the nearest ten-thousandth of a second? Why or why not?
No, it would not be appropriate to label the time axis to the nearest ten-thousandth of a second. This level of precision is unnecessary and impractical for the observation of motion in most real-world scenarios. The video likely does not capture or provide data with such a high level of accuracy in terms of time measurements. Labeling the time axis to the nearest ten-thousandth of a second would create an excessively detailed and cluttered graph, making it difficult to interpret and understand the relationship between distance and time accurately. It is more sensible and sufficient to use units that align with the level of precision and relevance of the data collected in the video.
Next, think of an event that might occur at three different speeds and describe it.
One event that can occur at three different speeds is driving a car on a highway. Let's consider the event of a car traveling from one city to another, a distance of 300 kilometers.
At a slow speed: The car sets off at a slow speed of 40 kilometers per hour. The driver maintains a consistent pace throughout the journey. As a result, the car takes a total of 7.5 hours to reach the destination.
At a moderate speed: The car takes the same route but now travels at a moderate speed of 80 kilometers per hour. With this increased speed, the car covers the 300-kilometer distance in only 3.75 hours.
At a high speed: Finally, the car decides to drive at a high speed of 120 kilometers per hour. With this accelerated pace, the car completes the journey in an even shorter time of 2.5 hours.
In summary, the event of driving a car from one city to another can occur at different speeds, resulting in varying travel times to cover the same distance. The slow speed can take 7.5 hours, the moderate speed reduces it to 3.75 hours, and the high speed further decreases it to 2.5 hours.
Select the most appropriate unit to measure the length of the California coastline.
yards
miles
meters
feet