Physics 1110 Fall 2004L3 - 1Lecture 3 27 August 2004 Announcements• Check the course web page for next week’s recitationassignment• Register your “clickers” via the link on the course web pageThe Velocity VectorIn the previous lecture we learned how to add and subtract vectorquantities using arrows to represent the vectors. Now we can usethese rules to find the displacement vector r = r2 r1. The positionvectors are shown in the first figure, while the calculation of thedisplacement is shown in the next figure.Note that the displacement is just the vector that points from positionof the object at time 1 to that at time 2, so it does not depend on thechoice of coordinate system or origin.Physics 1110 Fall 2004L3 - 2The average velocity is just the vector that describes that rate atwhich we made a displacement, and is defined simply as thedisplacement divided by the elapsed time:v rtThis is the average velocity over the time t. But what does it mean tomultiply or divide a vector by a scalar (a scalar is just a size withoutdirection)? The rule is simple in this case. The direction of the vectorstays unchanged and the magnitude of the vector is multiplied ordivided by the scalar, so that its length changes. For example if wemultiply the vector A by the number a to get the new vector C = aAthen C points in the same direction as A and C = aA. The figurebelow shows a simple example for the case of a = 2.In this case, we are doing more than just changing the length, sincewe are dividing by a number with units (time) so we get a really newquantity with units of length/time, in other words, a speed!There are a number of things to note here:• This is the physics definition of velocity and it is NOTsynonymous with the word speed. In physics we reserve theword speed to mean the total distance traveled divided by thetime elapsed. In the case of someone traveling east in astraight line 10 miles long for 1 hour, the velocity is 10 mpheast, the magnitude of the velocity it 10 mph, and the speed is10 mph. In the case that someone runs a 10 mile race in 1 hourover a course which returns the runner to the starting position,the speed is still 10 mph, but the displacement and henceaverage velocity are zero!Physics 1110 Fall 2004L3 - 3• On out motion diagrams with make the velocity arrows thesame length as the displacement arrows because it isconvenient. In fact, we could use a different scale and getdifferent length velocity arrows. Remember that you alwaysinterpret the length of the arrow using a scale (e.g. 1 inch = 25mph).• It makes no sense to add velocity vectors to displacementvectors! They are different things; it would be like adding 5years to 10 miles.Below are shown a 1D and a 2D example of displacement andvelocity vectors for some typical motion diagrams.Physics 1110 Fall 2004L3 - 4Note that in the future, we’ll stop showing the displacement, since thevelocity arrow gives the same information. Also, the arrow directionsshow the time order of the dots, so we may occasionally drop thenumerical subscripts, if they are not really needed.We now have vectors which precisely define position, the change inposition, and the average velocity (rate of change in position). Thesecorrespond roughly to the quantities we know in every day speech,but have the important distinction of being vectors, where size anddirection are not separated. In the next lecture, we will look at howvelocities
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