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http://www.stmary.ws/highschool/ physics/home/animations3/motion _graphs2.html Examples of Displacement vs. Time Graphs

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Distance vs. Displacement A leprechaun, searching for his Pot o’ Gold, scurries 50 m North in 10 s. With no luck in finding the gold, he decides to run 100 m West, taking him 15 s. Off in the distance, he sees a double rainbow (OMG! All the way!). Scampering to the end of the rainbow 250 m East, he finds his gold 20 s later. a) What is the total distance the leprechaun travels? b) What is the total displacement the leprechaun travels? c) Draw a distance v. time graph d) What is the velocity of the leprechaun from 0 – 10 s? e) What is the velocity of the leprechaun from 10 – 25 s? f) What is the velocity of the leprechaun from 25 – 45 s? g) What is the average velocity of the leprechaun?

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Answers a) Distance = 100 m + 50 m + 250 m = 400 m b) Displacement (y-axis) = 50 m North Displacement (x-axis) = 250 m – 100 m = 150 m East Displacement (resultant magnitude) =a 2 + b 2 = c 2 50 2 + 150 2 = c 2 Displacement (resultant) = rad(25 000) = c = 158.1 m Displacement (direction) = tanθ = opp/adj θ = tan -1 (150/50) θ = 71.6° East of North

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Answers (continued) c) d t 400 300 200 100 0 5 10 15 20 25 30 35 40 45

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Answers (continued) d)Velocity = displacement/time Velocity = 50 m/10 s = 5 m/s North e) Velocity = 100 m/15 s = 6.67 m/s West f) Velocity = 250 m/20 s = 12.5 m/s East g) v = distance/time = 400 m/45 s = 8.89 m/s

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Velocity A shopping cart is at rest at the top of a hill. A slight wind pushes the cart, causing it to start to roll down the hill with an acceleration of 3.2 m/s 2. a) How fast is the shopping cart moving after it has travelled a distance of 128.7 m? b) How much time did it take for the cart to reach 128.7 m? c) What would be the velocity at 257.4 m? d) How long does is take to reach 257.4 m?

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Answers a) Givens: v i = 0.0 m/s; a = 3.2 m/s 2 ; d = 128.7 m Unknown: v f = ??? Formula: v f 2 = v i 2 + 2ad Substitute with units: v f 2 = 0 m/s + 2*(3.2 m/s 2 )*(128.7 m) v f 2 = 823.68 m 2 /s 2 v f = 28.7 m/s The “*” indicates multiplication

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Answers (continued) b)Givens: v i = 0.0 m/s; a = 3.2 m/s 2 ; d = 128.7 m Unknown: t = ??? Formula: d = v i t + ½at 2 Substitute with units: 128.7 m = (0 m/s)t + ½(3.2 m/s 2 )t 2 128.7 m = (1.6 m/s 2 )t 2 t = rad(80.4375 s 2 ) t = 9.0 s

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Answers (continued) c)Givens: v i = 0 m/s; a = 3.2 m/s 2 ; d = 257.4 m Unknown: v f = ??? Formula: v f 2 = v i 2 + 2ad Substitute with units: v f 2 = 0 m/s + 2*(3.2 m/s 2 )*(257.4 m) v f 2 = 1647.36 m 2 /s 2 v f = 40.6 m/s

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Answers (continued) d)Givens: v i = 0.0 m/s; a = 3.2 m/s 2 ; d = 257.4 m Unknown: t = ??? Formula: d = v i t + ½at 2 Substitute with units: 257.4 m = (0 m/s)t + ½(3.2 m/s 2 )t 2 257.4 m = (1.6 m/s 2 )t 2 t = rad(160.875 s 2 ) t = 12.7 s

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