September 24, 2008 IOT POLY ENGINEERING I1-22 DRILL: A. DESCRIBE HOW THE AXES OF A GRAPH ARE LABELED PROPERLY. B. DESCRIBE HOW DATA POINTS ON A GRAPH ARE.

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September 24, 2008 IOT POLY ENGINEERING I1-22 DRILL: A. DESCRIBE HOW THE AXES OF A GRAPH ARE LABELED PROPERLY. B. DESCRIBE HOW DATA POINTS ON A GRAPH ARE PROTECTED FROM OBLITERATION WHEN DRAWING A LINE OR CURVE.

IOT POLY ENGINEERING I1-22 HERE IS THE COMPLETED CHART AND GRAPH FROM YESTERDAY’S PRINTED HANDOUT SHEET.

IOT POLY ENGINEERING I1-22 The engineer of an express train traveling at 30 m/s notices a freight train 84 meters up ahead traveling in the same direction at only 10 m/s. The engineer immediately puts on the brakes and the train decelerates at 2 m/s/s. Will the trains collide? Explain. If there is a collision, how many seconds after the engineer puts on the brakes will the trains collide? If there is not a collision, how far apart will the trains be when the express train finally stops?

IOT POLY ENGINEERING I1-22 This problem is very difficult, but can be solved with algebra and a graph. We need to determine if both trains are ever in the same place at the same time. We will calculate the distance of each train based upon the location of the express train when the brakes were applied. The distance traveled by the freight train is given by: D = t The distance traveled by the express train is given by: D = 30 t – t 2

IOT POLY ENGINEERING I1-22 The express train loses 2 m/s of speed every second, so we could assume that it will lose all 30 m/s of its original speed within 15 seconds. Now, let’s calculate where each train is located at t=15 seconds. D = t D = (15) = = 234 meters D = 30 t – t 2 D = 30 (15) – (15 2 ) = 450 – 225 = 225 meters The problem stated: “If there is not a collision, how far apart will the trains be when the express train finally stops?” Based on our assumption that the express train will stop in 15 seconds, we conclude that there is not a collision and the trains are 9 meters apart. Now, let’s solve the same problem using a graph.

IOT POLY ENGINEERING I1-22 For every second of time, determine the location of each train from the original location of the express train. The freight train starts at 84 meters, while the express train begins at 0 meters. Based on the graph of each train’s location, what is your conclusion? The trains collide at t=6 s. HERE IS THE COMPLETED CHART AND GRAPH FROM YESTERDAY’S PRINTED HANDOUT SHEET.

IOT POLY ENGINEERING I This is the normal boiling temperature of water at sea level. This is the normal freezing temperature of water at sea level. 320 This line represents any temperature on the thermometer. FC F - 32C F - 32C = We can now solve for either F or C. Let’s do both! We can set up a proportion: TEMPERATURE CONVERSION DERIVATION

IOT POLY ENGINEERING I1-22 F C = F = C 100 Cross Multiply 100(F – 32) = 180C Divide by GCF (greatest common factor) 5(F – 32) = 9C 5(F – 32) = C 9 This equation is used to solve for C when F is known. F – 32 = 9C 5 F = 9C This equation is used to solve for F when C is known.

IOT POLY ENGINEERING I KC A. BASED ON THIS DIAGRAM, DERIVE 2 EQUATIONS: 1. TO CONVERT KELVIN TO CELSIUS 2. TO CONVERT CELSIUS TO KELVIN. B. CAN THE FAHRENHEIT TEMPERATURE EVER MATCH THE CELSIUS TEMPERATURE? ( X F = X C ) USE ALGEBRA TO PROVE YOUR CONCLUSION. Study for Friday’s test on Unit 1. HOMEWORK - September 24, 2008