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Motion Graphs/Vectors

Motion Graphs/Vectors. Jeff, Jason, & Allie. Terms. Velocity – Rate of change of position . Acceleration – Rate of change of velocity . Speed – Ratio of distance traveled to the time interval. Distance – Scalar quantity equal to the sum of the magnitude of the displacements.

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Motion Graphs/Vectors

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  1. Motion Graphs/Vectors Jeff, Jason, & Allie

  2. Terms • Velocity – Rate of change of position. • Acceleration – Rate of change of velocity. • Speed – Ratio of distance traveled to the time interval. • Distance – Scalar quantity equal to the sum of the magnitude of the displacements. • Displacement – Vector quantity representing the change in position of an object. • Vectors – Arrows that depict direction and relative magnitude.

  3. Hjmnghdfghgfhgfdhgfdhdfghdgfhdg Constantly faster away

  4. Can you tell which car is moving quicker to the right?

  5. Sample Problem A plane flies 120 km/hr due east with a tailwind blowing east at 30 km/hr. What is the resultant velocity of the plane? 120 km/hr 30 km/hr EAST The vectors are connected head to tail! The quantities should be added together. 120 km/hr + 30 km/hr = 150 km/hr

  6. Sample Problem #2 If the same plane flew into a head wind, what would be its resultant velocity? WEST 120 km/hr 30 km/hr EAST The vectors are connected head to tail! The quantities should be subtracted, however. 120 km/hr - 30 km/hr = 90 km/hr

  7. But there’s more… A resultant vector can also be broken down into it’s vertical and horizontal components. However, not all things happen at exactly 90 degrees. Trigonometry can help with this! Opposite Sin = ----------------- Hypotenuse Adjacent Cos = ----------------- Hypotenuse Opposite Tan = ----------------- ADJ X Adjacent Hypot. Opp.

  8. Sample Problem #3 A boat travels east at 3.8 m/s and heads straight across a 240 m wide river. The river flows south at 1.6 m/s. What is the boat’s resultant velocity? What ANGLE is the boat traveling SE? 3.8 m/s (3.8)2 + (1.6)2 = C2 14.44 + 2.56 =C2 X C=4.12m/s 1.6 m/s C Sin X = 1.6m/s /4.12m/s X = 22.8 degrees

  9. Both can visually show change in speed and/or direction. Cars & Planes: Constant velocity, acceleration, change in direction, & stopping. Examples from the REAL WORLD:Motion Graphs & Vectors

  10. Draw in the Motion graph: Walking with a constant velocity & after a few seconds, walking constantly faster. V T

  11. Your Turn! * A plane flies due east at 250 km/hr. A wind carries it north at 50 km/hr. What is the magnitude and direction of the plane’s velocity? 254.95 km/hr NE * A flight of geese fly at 72 degrees southwest at 23 km/hr for winter. With what speed were the geese flying south? With what velocity were the geese flying west? 21.87 km/hr south 7.11 km/hr west * A plane flies 100 km/hr due west with a tailwind blowing west at 45 km/hr. What is the resultant velocity of the plane? 145 km/hr

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