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Displacement and Velocity. 2.1 pp. 40-47 Mr. Richter. Agenda. Warm-Up Review Pop Quiz Any Questions from the Lab? Introduce Motion Oil Drop Drawing Notes: Motion Displacement Velocity Average Velocity vs. Instantaneous Velocity Position vs. Time Representations
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Displacement and Velocity 2.1 pp. 40-47 Mr. Richter
Agenda • Warm-Up • Review Pop Quiz • Any Questions from the Lab? • Introduce Motion • Oil Drop Drawing • Notes: • Motion • Displacement • Velocity • Average Velocity vs. Instantaneous Velocity • Position vs. Time Representations • Oil Drop Diagrams • P vs. T graphs • Items of Business: • Skipping Section 1.3. Read it on your own if you want to. It’s boring. • Test Wednesday, October 3 • Measurements in Experiments (1.2) • Metric Prefixes • Accuracy and Precision • Scientific Notation and SigFigs • Displacement and Velocity (2.1)
Objectives: We Will Be Able To… • Describe motion in terms of frame of reference, displacement, time and velocity. • Calculate the displacement of an object traveling at a known velocity for a specific time interval. • Construct and interpret different representations of position versus time.
Warm-Up: • A car has an oil drip. As the car moves, it drips oil at a regular rate, leaving a trail of spots on the road.Which of the following diagrams of the car’s trail of spots shows the car continuously slowing down? How do you know?
Visual Representations of Speed Oil Drop Diagrams and Distance vs. Time Graphs
Group Drawing • At your table, use the whiteboard to show: • The oil drop diagram of a car that starts fast, slows down, then speeds up again. • Copy the diagram that represents the best representation into your notes. • Now, draw the distance vs. time graph of the same car. • Copy the graph that represents the best representation into your notes.
Diagrams (of Fast, Slow, Fast) Oil Drop Distance vs. Time Distance Time
Motion • A huge part of attempting to understand the nature of the universe is understanding how objects move: motion. • For now, we will only discuss one-dimensional motion. • Think of a train on a track. • Forward and backward (or left and right) only. Not up and down. Not coming closer or moving farther away. • In the future, we will look at motion in two dimensions by breaking it down into examples of one-dimensional motion. http://www.microsoft.com/games/trainsimulator/profile_settle_carlisle.aspx
Motion and Frames of Reference • Motion depends upon the frame of reference. • Is the train 20 km past Station 1, or 30 km away from Station 2? • Am I 5 m above the water, or 10 m below? • A frame of reference is a coordinate system for specifying the precise location of objects in space. • In other words, it’s where you put the origin (0, or in two dimensions, (0,0))
Motion and Frames of Reference • If an object is at rest (not moving), its position relative to its frame of reference does not change. • So, even though the earth is spinning, and rotating around the sun, and the sun is orbiting in our galaxy… • We are not moving (if you’re sitting in your seats right now), relative to our frame of reference.
Displacement • The change in position of an object. • The straight line distance drawn from an object’s initial position to its final position. • f stands for final, i stands for initial • Δ= “delta” = “the change in…”
Displacement • Displacement is not always equal to distance traveled. • If I move 5 meters to the right and then 3 meters to the left: • My distance traveled is 8 meters, but • My displacement is 2 meters to the right. • Distance is like what your odometer reads after you drive your route. • Displacement is how far away you are from where you started, no matter what route you took.
Displacement • Displacement can be positive or negative. • For our purposes (convention): • Displacement is positive if an object moves to the right or up • Displacement is negative if an object moves to the left or down
Velocity • Take 30 seconds to think about what the word “velocity” means to you. (definitions, types of…, units, etc.) • Then discuss with your tablemates. • We will discuss as a class in 1 minute.
Velocity • Motion is not completely described by where an object starts and where it stops. • How long it takes to get there is important as well. • Average velocity is the total displacement divided by the time interval during which the displacement occurred. • Displacement ÷ time = [meters/second] or [m/s]
Practice Problem • During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What distance does Andra cover in 137 s? • Δx= 825 m to the east (3 sigfigs)
Average Velocity • Why do we say “average” velocity? • The displacement divided by the time might not be the same as the velocity at any given instant. • That is: average velocity does not necessarily equal instantaneous velocity. • If I drive an average of 50 km/h to work, my speedometer probably does not read 50 km/h at every instant. • I should hope not! Stop signs!!
Negative Velocity • What does it mean if velocity is negative? • Just like displacement, velocity can be negative, too. • In fact, if your displacement during a time interval is negative, so is your velocity! • -10 m/s means that an object travels 10 meters to the left (or down) every second.
Velocity is not Speed • Speed is the distance traveled divided by the time interval, while velocity is the displacement divided by the time. • Example: If I drive 10 km to the grocery store and then 10 km back to my house, and it takes me 1 hour of driving time: • My average speed is 20 km/h • My average velocity is 0 km/h (no displacement = no velocity)
