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STARTER During a road trip, in 6 hours you travel 300 miles. What is your average velocity? Average Velocity = distance travelled/time taken = 300 miles/6 hours = 50 miles/hr

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Graphing Motion Distance vs. Time Velocity vs. time Acceleration vs. time

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Displacement x x = x f - x i In this case, x i = -1m, x f = 3m, So x = 3 – (-1) = 4m

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Average Velocity v avg V avg = x / t In this case, x i = -1m, x f = 3m, so x = 3 – (-1) = 4m, and t = 4 – 0 = 4s. So, v avg = 4m/4s = 1m/s

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Average velocity is the slope of the x vs. t graph. Compare the velocities for the three graphs. The graph tells you 1.The direction of motion. 2.The relative speed.

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Changing Velocity Car 1 time(s)Velocity(m/s) 05 210 415 620 825 How much does the velocity of this car change every second? (+5m/s) / (2 s) or 2.5 m/s/s

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Changing Velocity How much does the velocity of this car change every second? (+10m/s) / (2 s) or 5.0 m/s/s Car 2 time(s)Velocity(m/s) 010 220 430 640 850

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Changing Velocity How much does the velocity of this car change every second? (+0m/s) / (2 s) or 0 m/s/s Car 3 time(s)Velocity(m/s) 0100 2 4 6 8

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Changing Velocity How much does the velocity of this car change every second? (-5m/s) / (2 s) or -2.5 m/s/s Car 4 time(s)Velocity(m/s) 040 235 430 625 820

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These rates are called accelerations: a = v / t The acceleration of an object tells you how much the velocity changes every second. The acceleration of an object tells you how much the velocity changes every second. The units of acceleration are m/s 2.

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The acceleration is the slope of a velocity vs. time graph. a = v / t = rise / run = 3/5 m/s 2. a = v / t = rise / run = 3/5 m/s 2. + slope = speeding up -slope = slowing down zero slope = constant speed

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From a Description to a Graph. An object at x = 1m, stays at rest for 2 seconds, then moves at 1m/s for 3 seconds, then stops for 1 second. Sketch a distance vs. time graph of this motion. An object at x = 1m, stays at rest for 2 seconds, then moves at 1m/s for 3 seconds, then stops for 1 second. Sketch a distance vs. time graph of this motion. For t = 0 to t = 2, x is always 1m. For t = 2 to 5, the slope is 1. Then the slope is zero For 1 second. Give it a try.

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Here it is.

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Now do a v vs. t graph for the same motion.. Remember, the velocity is the slope of the x vs. t graph. Remember, the velocity is the slope of the x vs. t graph. For t = 0 to t = 2, the slope is zero. For t = 2 to 5, the slope is 1. Then the slope is zero for 1 second. Give it a try.

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Here it is.

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Description from a Graph Give a description of this motion.

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For the first 3 seconds the object moved ___________ at a speed of _________m/s. For t = 3 to 5, the object___________________________________. For the last 3 seconds the object moved ___________ at a speed of _________m/s.

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Summary Displacement x = x f - x i Average Velocity V avg = x / t Acceleration a = v / t Average velocity is the slope of the x vs. t graph. Acceleration is the slope of the v vs. t graph. The graph tells you 1.The direction of motion. 2.The relative speed The acceleration of an object tells you how much the velocity changes every second.

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