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Linear Motion

Linear Motion. Jumpstart. Calculate the acceleration of a car that is traveling from 80 m/s to 0/s in 20 seconds. Kinematics. Branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion. Motion is relative.

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Linear Motion

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  1. Linear Motion

  2. Jumpstart • Calculate the acceleration of a car that is traveling from 80 m/s to 0/s in 20 seconds.

  3. Kinematics Branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion.

  4. Motion is relative • Measured in reference to another object or point. • Depends on Frame of Reference. • How fast is your body moving right now?

  5. How far did you go? • Distance • Needs no frame of reference • Separation between two points • Only a length, no direction • Scalar Quantity • Units: • Meters, kilometers, centimeters. . . .

  6. B A D C What is your new position? • Displacement • Change in position. • Where are you relative to some starting point? • Magnitude and direction • Vector Quantity • Express direction with a sign or direction • 45m to the North • -82 cm

  7. The difference between distance and displacement. . . . .

  8. Speed • How fast something is moving. • Speed = distance/time • Units: m/s, km/h, mph. . . • Scalar Quantity • Instantaneous speed • Average speed • Over the course of a trip, can instantaneous speed and average speed be different from each other?

  9. Approximate Speeds in Different Units

  10. Velocity • Speed in a given direction. • Vector quantity • Magnitude AND direction • Velocity = displacement/time • V = d/t • Units = m/s, km/h, mph. . . • Direction expressed with • Signs: + or – • Direction: North, South, East, West, Left, Right, Forward, Backward. . .

  11. A change in velocity is called. . Velocity • Constant Velocity • constant speed and direction • Changes in velocity are due to • Increase/decrease in speed • Change in direction • If you drive around a circular track with a constant speed of 60 km/h, is your velocity also constant?

  12. Velocity • Instantaneous Velocity • Average Velocity

  13. Example Problems • A team begins play on the 50 yard line; they lose 5 yards on a play and then gain 15 yards on the next play. • What distance did the team travel? • What was the team’s displacement? • A truck travels 300km north in 10 hours. What was the truck’s average velocity?

  14. Example Problems • How long would it take you to drive 15 km a rate of 30 km/h?

  15. Acceleration • The rate of change of velocity. • Equal to the change in velocity divided by time. • a = (vf – vi)/t OR a = Δv/t • Units: • Meters per second per second (m/s/s) • Meters per second squared (m/s2) • If a car can accelerate from 0-60mph in 15 seconds, what is its acceleration? (60mph – 0 mph) / 15s = 4 mph / s2

  16. Acceleration • Vector quantity • Has both magnitude and direction • Direction expressed with a sign (+/-) • Can refer to: • Increase in speed • Decrease in speed • Change in direction

  17. Acceleration • If speed increases while you are moving forward, acceleration is positive. • If speed decreases while you are moving forward, acceleration is negative • Example 1: You are driving and increase your speed from 50 m/s to 75 m/s in 10 seconds. What is your acceleration? 75 m/s – 50 m/s = 25 m / s = (2.5 m / s2) 10 s 10 s

  18. Acceleration • Example 2: You are riding your bike and slow from 10 m/s to 5 m/s in 2 seconds. What is your acceleration? • Example 3: How long will it take to accelerate from 20 m/s to 40 m/s if your velocity changes at a rate of 4 m/s2?

  19. Position-Time Graphs • Position on the y-axis, time on the x-axis. • Position is measured with respect to a reference point; therefore position can increase or decrease. • Slope of the line is velocity.

  20. Position-Time Graphs

  21. Position Time Graphs

  22. Position Time Graphs

  23. Position-Time Graphs

  24. Average Velocity Instantaneous Velocity Instantaneous Velocity Instantaneous Velocity Position-Time Graphs

  25. Position-Time Graphs Curve = changing velocity Constant Acceleration = Curve Straight Line = constant velocity

  26. Position Time Graphs Constant + v, slow Constant + v, fast Constant –v, fast Constant –v, slow

  27. Positive acceleration (increasing velocity) in the negative direction Negative acceleration (decreasing velocity) in the negative direction Position-Time Graphs

  28. Position-Time Graphs

  29. Velocity-Time Graphs • Time on the x-axis (s) • Velocity on the y-axis (m/s) • Slope is acceleration (m/s2) • Area under graph represents displacement. • It line is curved – the acceleration is changing

  30. Slope of the graph is important: Slope = 0 (Horizontal line) Velocity is constant Positive slope Velocity is increasing Negative slope Velocity is decreasing Shape of the graph is important Straight line: acceleration = 0 Velocity may be 0 Velocity may be constant Curve Acceleration is changing Velocity-Time Graphs

  31. Increasing Velocity Constant +Acceleration What was this object’s displacement? Velocity-Time Graphs

  32. Decreasing Velocity Constant -Acceleration Velocity-Time Graphs

  33. Increasing Negative Velocity Constant -Acceleration Velocity-Time Graphs

  34. What do you think? If you are given a table of velocities of an object at various times, how would you determine if the acceleration of the object was constant?

  35. Decreasing Negative Velocity Constant +Acceleration Velocity-Time Graphs

  36. HOW COULD YOU DETERMINE: • Average Velocity? • Instantaneous acceleration? Velocity-Time GraphsWed. 10/10/12

  37. Increasing Velocity Positive Acceleration Velocity-Time Graphs

  38. Average Acceleration Instantaneous Acceleration Instantaneous Acceleration Instantaneous Acceleration Velocity-Time Graphs

  39. Constant velocity (v=40m/s) Zero Acceleration Constant velocity (v=0m/s) Zero Acceleration Velocity-Time Graphs

  40. Acceleration-Time Graphs

  41. Acceleration-Time Graphs

  42. Acceleration-Time Graphs

  43. Constant Rightward Velocity • Website Animation

  44. Constant Leftward Velocity

  45. Rightward Velocity/Rightward Acceleration

  46. Rightward Velocity/Leftward Acceleration

  47. (10/10/12) Wednesday • Sketch a position vs. time , velocity vs. time and an acceleration vs. time graph for each of the following two situations. • Leftward velocity and rightward acceleration • Leftward velocity and leftward acceleration

  48. Leftward Velocity/Rightward Acceleration

  49. Leftward Velocity/Leftward Acceleration

  50. And now for the calculations . . . • Assume acceleration is constant • Either zero or some non zero value. • Variables • a = acceleration • v0 = initial velocity • v = final velocity • d = displacement • t = time

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