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Mechanics - Kinematics

Mechanics - Kinematics. Define : Displacement – distance & direction from reference point D x , D y , D z . Pos or neg sign gives direction. V elocity – rate & direction object changes in position D x /t or s/t. sign follows displacement.

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Mechanics - Kinematics

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  1. Mechanics - Kinematics • Define: • Displacement – distance & direction from reference point Dx, Dy, Dz. • Pos or neg sign gives direction. • Velocity – rate & direction object changes in position Dx /t or s/t. • sign follows displacement. • Acceleration – rate change of velocity Dv /t. • Sign give change in vel – not direction.

  2. Velocity • Average velocity = s tot/ t tot. • Instantaneous velis a limit. • Can find from slope of tangent to point.

  3. Ex 1: A bus travels north 180 km in 2.2 hours. It stops for 30 minutes turns and drives 60 km south in 45 min. What is its average velocity in km/h. • vav = stot / t tot. • 34.8 km/h.

  4. Kinematics Equations • IB Tables pg 6 • Uniform/constant acceleration: Dv same increment. • u = vi • v = vf • s = displ. • a = Dv/t

  5. Acceleration of gravity g remarks. • Constant/uniform -9.81 m/s2on Earth. • Negative sign is arbitrary! • Often use 10 m/s2 as estimate. • Air resistance in atmosphere causes objects to reach terminal fall velocity after falling for a time. • Wind/Air resistance increases with speed. Fuel efficiency in cars better at slower speeds.

  6. Relative Motion Ex 2: • You are standing on a railway platform. A is train moving at 25 m/s to the right. On it is a passenger walking to the right at 2 m/s. What is his velocity relative to you? • 27 m/s. • If the velocity of object A, relative to a fixed point is VA, the velocity of object B, relative to the same fixed point is VB, then the velocity of A relative to B is the vector difference: is VA - VB.

  7. Ex 3: Car A is traveling 15 m/s and is overtaken by car B which is moving in the same direction at 18 m/s. What is the velocity of car B relative to car A? • Vb – Va = • 3 m/s. • What is the velocity of Car A relative to Car B? • Va– Vb- 3 m/s

  8. Ex 4: A boat heads north across a river 90 m wide. The speed of the boat relative to the shore is 1.8 m/s but the river pushes the boat east at 1.2 m/s. A) What is the speed of the boat relative to the water?B) How far will it land downstream when it arrives at the opposite shore? • 2.2 m/s • 60-m.

  9. Practice Sheet “IB Kinematics Questions”

  10. IB Motion Graph Review

  11. Distance/Position/Displacement Time GraphsConstant vel. Slope = Velocity Slower Velocity Starting point

  12. Positive Negative Quadrants Where object is w/ref to starting point.

  13. What is the object’s: • a. displacement • distance 10 30

  14. Constant Velocity/Speed

  15. Constant / Uniform Acceleration. On velocity time graph accl. is slope of straight line. + or neg a shown?

  16. What’s going on here physically?

  17. Sign of velocity is direction of motion shown by the quadrant. What does this show?

  18. What does -v mean?

  19. What does the sign of slope mean?

  20. Displacement = Area Under Curvev = d/t then, vt = d.

  21. To find displacement, calc area of triangle + rectangle.

  22. When is object back at start point? + area must = - area

  23. Acceleration – time graphs Graph d-t, v-t, a-t tossed ball & caught at same height.

  24. In Class. Kerr pg 39 Ex 2.1 #1Hwk Kerr pg 71 Topic 2.1 #1-4.

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