D. Roberts PHYS 121 University of Maryland Physics 121: Fundamentals of Physics I September 8, 2006

D. Roberts PHYS 121 University of Maryland Announcements / Reminders Next homework is available on WebAssign –Free WebAssign use expires next Wednesday! Tutorials (Discussion Sections) and Labs will begin meeting next week

D. Roberts PHYS 121 University of Maryland Outline Example Dimensional Analysis Problem Describing Motion: –Coordinates in space and time The idea of velocity –average velocity –instantaneous velocity –graphing velocity

D. Roberts PHYS 121 University of Maryland Dimensional Analysis In the following equation, determine what the dimensions of  have to be in order for the equation to be physically meaningful: where [ v ]=L/T, [ x ]=L and [ m ]=M –L is length –M is mass –T is time

D. Roberts PHYS 121 University of Maryland Describing Motion: Space Coordinates — telling where something is What do we need to do to specify the location of something so someone else can find it? –Note the difference between “length” or “distance” and “position” –Representing a position mathematically.

D. Roberts PHYS 121 University of Maryland Coordinates and Vectors Set up a coordinate system –Pick an origin –Pick 3 perpendicular directions –Choose a measurement scale Each point in space in then specified by three numbers: the x, y, and z coordinates. The position vector for a particular position is an arrow drawn from the origin to that position.

D. Roberts PHYS 121 University of Maryland Motion along a straight line (1-d coordinates) We specify which direction we are talking about by drawing a little arrow of unit length in the positive direction. We specify that we are talking about this arrow in symbols by writing A position a distance x from the origin is written Note that if x is negative, it means a vector pointing in the direction opposite to

D. Roberts PHYS 121 University of Maryland Describing Motion: Time Time — if we’re to describe something moving we need to tell when it is where it is. Time is a coordinate just like position –We need an origin (when we choose t = 0) –a direction (usually times later than 0 are +) –a scale (seconds, years, millennia) Note the difference between –clock reading –a time interval This is like the difference between position and length!

D. Roberts PHYS 121 University of Maryland Writing the math Position at a clock time t: (if we want to emphasize the direction) Position at a clock time t: (if we don’t) Change in position between two times (t 1 and t 2 ): Time interval:

D. Roberts PHYS 121 University of Maryland Graphing Position Describe where something is in terms of its coordinate at a given time.

D. Roberts PHYS 121 University of Maryland Displacement The displacement is the total change in position. If you make one change and then go back, it could cancel out the first change.

D. Roberts PHYS 121 University of Maryland Displacement Isn’t Distance The displacement of an object is not the same as the distance it travels –Example: Throw a ball straight up and then catch it at the same point you released it The distance is twice the height The displacement is zero

? Below is shown a straight track along which a toy train can move. If the train moves from point A to point C and then back to point B, what is its resulting displacement (in feet)? x A C B feet 1.2 feet 2.3 feet 3.5 feet 4.12 feet 5.None of the above

D. Roberts PHYS 121 University of Maryland Example Below is shown a straight track along which a toy train can move. If the train moves from point A to point C and then back to point B, what is its resulting displacement (in feet)? x A C B feet

D. Roberts PHYS 121 University of Maryland Average Velocity We need to keep track not only of the fact that something has moved but how long it took to get there. Define the average velocity by

D. Roberts PHYS 121 University of Maryland 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 PHYS 121 University of Maryland Instantaneous velocity Sometimes (often) an object will move so that it is not in uniform motion. Sometimes it moves faster, sometimes slower, sometimes not at all. We want to be able to describe this change in motion also. If we consider small enough time intervals, the motion will look uniform — for a little while at least.

D. Roberts PHYS 121 University of Maryland Example 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?

D. Roberts PHYS 121 University of Maryland 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. You can see this by putting your mind in “velocity mode” and running a mental movie.