1. Displacement Time Graphs Uniform and Non-Uniform Motion

2. Think about… Sketch a position-time graph of each object listed below. Describe its slope as positive or negative, and as constant, increasing, or decreasing. A) a stone at rest B) a jogger moving steadily to the right C) a bicycle moving to the left and slowing down D) a rocket moving up at an increasing speed E) a stone falling freely with increasing speed F) a parachutist drifting down at a steady speed

3. Uniform Motion You discussed mostly uniform motion (at least graphically) in Science 10. Uniform motion is represented by straight lines on a d-t graph. It describes objects moving with CONSTANT velocity and therefore no acceleration.

4. Instantaneous Velocity When you are driving on the highway and you look down at your speedometer, you are traveling at + 55 km/h. At that instant in time, + 55 km/h is your instantaneous velocity. For uniform motion, your instantaneous velocity is the same as you average velocity. For non-uniform motion, your instantaneous velocity changes constantly. This is true for most daily situations like driving.

5. Non-Uniform Motion An object does not always move at a constant speed or velocity. –Examples: Going around a race course –Merging on a highway –Braking at a stop sign You may speed up, slow down, or change directions. Non-uniform motion, when graphed, appears as a curve not a straight line.

6. Reminders… 1) How do you find velocities on a graph? 2) How do you find instantaneous velocities on a graph? 3) How do you find average velocities on a graph?

7. Finding Instantaneous Velocity from a Graph (Uniform Motion) To find instantaneous velocity on a uniform position- time graph, just find the average velocity for the given segment.

8. Finding Instantaneous Velocity from a Graph (Non-Uniform Motion) To find instantaneous velocity on a non- uniform position-time graph, draw a line that is tangent to the curve at that point. The slope is the instantaneous velocity (take the two points on the tangent from each side of the point).

9. http://en.wikipedia.org/wiki/Tangent

10. Non-Uniform Velocity: Summary Appears as a CURVE on a d-t graph Instantaneous velocity changes as you slow down, speed up, or change direction. Means acceleration is happening

12. Instantaneous Velocity (Non- uniform Motion)

13. Summary: Finding Instantaneous Velocity on a d-t graph Uniform Acceleration –Find the slope of that SEGMENT Non-Uniform Acceleration –Draw a TANGENT at that point TANGENT: just skims the curve at the point –Find slope of the tangent line by using 2 points (you can include the point on the curve but you don’t have to) –Finding the slope is easiest if you use points that are easy to read

14. Worksheet

15. Project