Speed at an Instant

A cart speeds up with a constant acceleration along a track. The table below shows the cart’s position at different times as read by a stop-watch.

Position

2ft

4ft

10ft

20ft

34ft

Stopwatch

Reading

0.0s

1.0s

2.0s

3.0s

4.0s

What is the speed of the cart at the instant when the stopwatch reads 2.0s?

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Some classic stuff here, but I wanted to try to bring this back alive.

  • What were these students thinking? How did they decide to make these particular marks on the page?
  • What do this work seem to suggest about what the students know? What ideas are they likely still struggling to make sense of?
  • What kinds of instruction would be warranted if such mistakes were limited to a few individuals?
  • What kinds of instruction would you want to have in place if a significant fraction of your students were making these mistakes?
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