This document provides an overview of key concepts in motion in one dimension including: 1) Frame of reference establishes the axis and defines where zero position is and the positive direction of motion. 2) Position is measured as a number line from the zero point. Displacement is the change in position between two points, regardless of path, while distance considers the actual path traveled. 3) Time intervals are defined similarly to displacement as the difference between two time points. Average velocity is displacement over time interval while instantaneous velocity considers an infinitesimally small time interval.

1. Motion in One Dimension Unit 2 Lesson 1 E. Alexander Burt Potomac School

3. Position is a measurement – a coordinate, really. A coordinate without an axis is meaningless!

5. Which way is positive?

7. We usually use the variable x for position

8. With more than one position to keep track of, we'll use subscripts, such as x 1 , x 2 or x i , x f or even x 0 , x

10. D x = x 2 – x 1

11. Note that it does not matter how the object gets from x 1 to x 2 . We do not consider the path at all.

12. Displacement may be positive or negative

13. Distance does consider the path and is always positive

15. D t = t 2 – t 1

16. Very often, t 1 will be zero

17. Negative time intervals are very very very rare.

19. Speed has a similar definition except that it's distance divided by time

21. We call that the instantaneous velocity. The actual definition uses the mathematical idea of a limit