Motion#
Example 3: area calculation of speeds#
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Go back to our original, idealized trip at a constant speed of 60 mph. The figure (a) on the left was our area calculation of the distance traveled at that constant speed and we can see that the boxes tell us that it took 5 hours.
Let’s look at a part of that trip, say the distance between Saginaw and Grayling (S-G) which is 100 miles. Estimate how long it takes to make that part of the ideal journey. Think in terms of multiplication using rectangles. (You can print out the figure and draw boxes it on the diagram.)
What you need to do is distribute 20 mile-sized rectangles until you’ve used up 100 miles-worth. (The left hand diagram was for 300 miles.) But, you’re moving at a constant 60 mph, so your rectangle collection has to always touch the 60 mph level.
Notice that the rectangles above don’t neatly match these parameters so you’d need to shrink some of them to be less than 20 miles-worth here. So your combinations will include some full boxes and some fractional boxes.
How many full boxes did you use to make the full 100 miles?