Displacement Time Graphs Uniform and Non-Uniform Motion

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

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.

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.

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.

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?

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).

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

Instantaneous Velocity (Non- uniform Motion)

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

Worksheet

Project