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physi 1300

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physi 1300

1. 1. Physics 130 Lecture 10 Motion-Velocity In one dimension Chapter 2
2. 2. Example <ul><li>Suppose I get on Interstate 80 and travel East at 65 miles per hour. (Simplify by assuming that I80 is straight!) </li></ul><ul><li>After 1 hour I will be 65 miles to the East </li></ul><ul><li>After 2 hours I will be 130 miles to the East etc. </li></ul><ul><li>Notice if I had gotten on I 80 travelling west, then </li></ul><ul><li>After one hour I would have been -65 miles East, </li></ul><ul><li>i.e. West is the negative of East. </li></ul>
3. 3. Velocity and Speed <ul><li>65 miles per hour is a SPEED </li></ul><ul><li>65 miles per hour East is a VELOCITY </li></ul><ul><li>-65 miles per hour East is 65 miles per hour West </li></ul><ul><li>VELOCITY has direction-it is a VECTOR </li></ul><ul><li>Speed is the Magnitude of the Velocity Vector </li></ul>
4. 4. Velocity-Average <ul><li>Velocity is the rate at which I change position </li></ul><ul><li>50 mph= 100 miles/2 hours </li></ul><ul><li>This is the average velocity over a 2 hour period </li></ul><ul><li>BUT this need not be your present speed </li></ul><ul><li>Example-if I travel for 1/2 hour at 35 mph and for 3/2 hour at 55 miles per hour </li></ul><ul><li>I will travel a total distance of 100 miles, and my average velocity will be 50 miles an hour-at which velocity I was almost never travelling! </li></ul><ul><li>PICTURES </li></ul>
5. 5. Velocity-Instantaneous (1-d) <ul><li>For this reason we DEFINE velocity as </li></ul>
6. 6. Velocity to Displacement <ul><li>In the first two examples we see that </li></ul><ul><li>If the velocity changes-the distance travelled becomes a sum over the velocities multiplied by the times </li></ul>
7. 7. Continuous Velocity <ul><li>Suppose the velocity is changing continuously </li></ul><ul><li>v(t)=vo+at, for example </li></ul><ul><li>Then the distance travelled will be the AREA under the velocity vs time curve-diagram </li></ul>
8. 8. Constant Acceleration Example <ul><li>PICTURES-REFER to LAB </li></ul><ul><li>If v(t)=v o +at </li></ul><ul><li>Then the area under the “curve” is </li></ul>
9. 9. Acceleration <ul><li>Acceleration (instantaneous) is the Rate of Change of the Velocity </li></ul><ul><li>If acceleration is constant then </li></ul><ul><li>Example: a steelball is dropped from the roof of a 30m building-it accelerates at 9.8m/s 2 </li></ul><ul><li>V=0-9.8t </li></ul><ul><li>Y=30-(1/2)9.8t 2 =>hits the ground (y=0) in sqrt(2*30/9.8)=2.47 seconds </li></ul><ul><li>At a velocity of -9.8(2.47)=24.25m/s </li></ul>
10. 10. Quiz <ul><li>A car accelerates from 0 to 25m/s in 10 seconds </li></ul><ul><li>(assume Acceleration is constant) </li></ul><ul><li>What is its acceleration? </li></ul><ul><li>How far does it travel? </li></ul>