Analysis of a Position vs. Time Graph

Determining the motion on a D vs. T Graph Where did the object start? Which direction did it go? Where did the object stop? Is the motion uniform (constant)? Is the motion non-uniform (changing)? Can you tell which is faster? (if 2 or more objects are present)

Position vs. Time Graphs & Velocity We can calculate velocity using Position vs. Time Graphs Velocity is a vector quantity because it has both magnitude & direction. It tells us not only the speed that an object is traveling, but also its direction Distance Rise Velocity = ----------- = ------- Time Run

Using slope to predict motion On a distance vs. time graph If slope is 0, then velocity is 0. If slope is positive, velocity is constant in positive direction. If slope is negative, velocity is constant in the opposite direction. If slope is changing, velocity is changing.(i.e. you are accelerating)

Object A is stationary at some positive position from the origin. d(m) A Object A is stationary at some positive position from the origin. t(s)

Object B moves away from origin with a constant positive velocity. d(m) B Object B moves away from origin with a constant positive velocity. t(s)

d(m) C Object C start at some positive position and moves away from the origin at a constant positive velocity. t(s)

d(m) Object D moves away from the origin at a constant positive velocity (slower than previous examples). D t(s)

d(m) Object E start at some positive position and walks toward the origin with a constant velocity. E t(s)

Distance vs. Time Graphs with Non-Uniform Motion Changing velocity (speeding up) Changing velocity (slowing down)

Example

Same velocity as B. Constant +V V=0 Slower than B or C. d(m) C B A D t(s)

PRACTICE

Practice #1 Imagine you are riding your bike down Detroit Rd. Compare the lines A-D Think of magnitude & direction!

A B C D Route 83/ Center Rd. Nagel Rd. (East) Stoney Ridge (West) A- moving at a constant rate east B- moving west to east past 83 at a constant rat (slightly slower than A) C- Sitting still at 83 D- moving east to west at a constant rate past 83 D Stoney Ridge (West)

Practice #2 Determine the Time & Distances for the graph below Time (s) Position (m) 2.5 5 7.5 10 12.5 0s=0m 2.5s=2.5m 5s=5m 7.5s=5m 10s=5m 12.5s=0m

Practice #3 Calculate the velocities for the following: Distance, m East Distance, m O-A= 2 m/s E A-B= 0 m/s (at distance 10m) B-C= 3.33 m/s West C-D= 0 m/s (at distance 0) D-E= 1 m/s East E-F= 0 m/s (at distance 5m)

Practice #4 Match the story to the graph below C