Discover it yourself:
Map-based motion at any speed
Level Two: This page continues a journey begun to discover 20th century methods for describing motion. It is designed like a multiple choice MAZE with challenges along the way that depend a good deal on the strategies that YOU adopt.
Just as we specified frame of motion (e.g. map versus pilot) in quantifying distance between sneezes, we also specify frame of motion when discussing time intervals (e.g. between two sneezes). This is an excellent habit for those wanting to understand high-speed motion and curved space-time. Only minor changes to 20th century intro-physics textbooks would be needed to set an example...
Recall that as our pilot approaches the red and then orange clocks in her flight path, she begins to feel a sneeze coming on.
The first sneeze occurs over the red clock, precisely when the red clock reads exactly 10 minutes after 10 am. When our pilot later sneezes over the orange clock 141 meters of map-distance further along on her voyage, that clock reads 10 minutes and 7 seconds after 10am. Thus the map-time elapsed between sneezes is seven seconds.
Question for YOU: If we define coordinate-velocity as the map-distance traveled per unit map-time elapsed, what is the average coordinate-velocity of our plane between sneezes?
Hint: Clear thinking about velocities and their rates of change was one key to moving from Aristotle's view of motion, to that of England's Isaac Newton, with help from Italy's Galileo Galilei. One way to check YOUR thinking is to note that velocity units arise whenever one divides something in meters by something in seconds. Another way is to get a pilot's license, borrow an airplane with a VERY LOW stall speed, and the persuade two bystanders to man stopwatches on the ground! Yet a third strategy (for those of us who like to visualize what's happening) might be to draw a graph of map-distance traveled versus map-time elapsed. The slope of a line drawn between (0 seconds, 0 meters) and (7 seconds, 141 meters) has something to do with the answer to this question.
Number of visits here since last reset is 
.
This Discover-It-Yourself Series is Copyright 1987-1997 by P. Fraundorf,
Department of Physics & Astronomy, University of Missouri - St. Louis.
Send comments and/or questions to pfraundorf@umsl.edu.