Physics 121 Fundamentals of Physics I September 11

Physics 121: Fundamentals of Physics I September 11, 2006 D. Roberts

From Last Time… • Displacement = Change in Position – Displacement is a vector, direction (or sign in 1 D) is important – Distance is not a vector • Like car odometer • Average Velocity = Displacement divided by Time Taken – Velocity is a vector, direction (or sign in 1 D) is important – Speed is not a vector D. Roberts

Graphing Position • Describe where something is in terms of its coordinate at a given time. D. Roberts

Uniform motion • If an object moves so that it changes its position by the same amount in each unit of time, we say it is in uniform motion. • This means the average velocity will be the same no matter what interval of time we choose. D. Roberts

After it is wound and released, a wind-up car travels at almost a constant velocity. Assuming it takes a negligible time to get up to speed, what does the graph of its velocity look like as a function of time? ? 1. 2. 3. 4. 5. 6. 1 Graph One Graph Two Graph Three Graph Four Graph Five None of the above 2 3 4 5

Graphing Velocity • An object in uniform motion has constant velocity. • This means the instantaneous velocity does not change with time. Its graph is a horizontal line. D. Roberts

Graphing velocity: From the position graph • You can also figure out the velocity graph from the position graph using Slope = <v> Dx Dt D. Roberts

Average Velocity, Non Constant • The motion is nonconstant velocity • The average velocity is the slope of the blue line joining two points • Instantaneous velocity is slope if tangent line (green lines) at a point D. Roberts Dt Dx

Interpreting Position vs. Time Graphs • Steeper slopes correspond to faster speed – Flat implies standing still • Negative slopes -> negative velocity (motion to the left) • The slope is the ratio of intervals, Dx/Dt, not a ratio of coordinates (not x/t) • Be sure to look at the scale on the x-axis (time) and y-axis (position) – Also, make sure you know where the origin is D. Roberts

A person initially at point P in the illustration stays there a moment and the moves along the axis to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to P. Which of the position vs. time graphs below correctly represents the motion? ? 1 2 Q R P 0 1 2 3 1. 2. 3. 4. 5. 6. Graph One Graph Two Choice Three Graph Four Choice Five Graph Six 3 4 5 4 position (arbitrary units)

? Consider the following velocity vs. time graph. Write down a description of the person’s motion with as much detail as possible. At the end of the motion, the person’s displacement is: 1. 2. 3. 4. 1 2 Positive Negative Not enough information None of the above 3 4 5