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Linear Motion

Explore the fundamentals of kinematics, acceleration, velocity, and displacement in the context of linear motion in physics. Learn the basic principles and calculations involved in understanding the motion of objects in different frames of reference.

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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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