Drawing Velocity Time Graphs from Position Time Graphs

Uniform and Non-Uniform Motion

• How can we use d-t graphs to determine v-t graphs?

• Find the velocity for each section of the graph and plot it (make a list of points).

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

Non-Uniform Motion

• An object does not always move at a constant speed.

• You may speed up or slow down.

• Non-uniform motion, when graphed, appears as a curve not a straight line.

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.

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.

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).

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

Instantaneous Velocity (Non-uniform Motion)

Page 57

• Page 57, question 4

• Page 58, question 5

• Worksheet