Motion

1. Motion

2. What is Motion? any physical movement or change in position or place, relative to a reference point  Movement Reference Point

3. Distance = how far an object has moved. Measured in meters, kilometers (cm or mm) If each mark represents 10 cm, what is the distance between the girl and the ball?  ______ Y Axis X Axis

4. If the girl walks to the red ball, then walks backwards to the bear, how far has she traveled?   ______ Y Axis X Axis Displacement = the distance of a body's change in position from a starting point.   Her final displacement is   ______ from the starting point.

5. Speed = the distance an object travels per unit of time  (sec, hour, year..etc) Speed Equation Speed (meters/second)  =  distance (in meters)                                                   time (sec)   s = d/t

6. A second car travels a distance of 100 meters in 20 seconds.  What is this car's speed?   A car travels a distance of 500 m in 10 sec.  What is the car's speed? s = d/t

7. More practice.  (Speed = distance/ time) An elevator travels from the first floor to the 25th floor of a building, a distance of 180 meters, in 60 seconds. What is the elevator's speed? Find the Distance = ______ Find the Time = _______ Calculate the Speed =  _______

8. Constant Speed vs Changing Speed  Constant speed means that the speed stays the same throughout the entire distance *Very few things can stay at a constant speed.  Rather, things usually move at a constant speed for a period of time.  The cyclist speeds up, slows down, stops..etc

9. Average Speed = total distance traveled                                       time taken This is useful when you are trying to measure speed, and the object moved at varying speeds throughout the trip.  For instance, if you drove from here to Chicago, you might AVERAGE 60mph, even though you stopped at lights, or slowed down or when 70 at some points on your trip.

10. On graphs that show distance and time, the SLOPE of the line is a measure of the speed of an object.

11. 1.  Calculate each turtle's speed: Bill ______ Myrtle ______ Zed ______

12. 2.  Can you find from the graph, the point where Zed stopped and floated for a while? 2.  Can you find from the graph, the point where Zed stopped and floated for a while? 3.  Which turtle wins the race? 4.  At what time period was Bill and Myrtle's speed the same?

13. How can you measure the speed of a mealworm?

14. Graphs represent speeds of objects.  This graph shows a bus as it travels its route.   Between what points is the bus accelerating? _____  &  ____ Between what points is the bus moving at a constant speed?                                                                _____  &  _____ Between what points is the bus stopped?  __________ Between what points it the bus decelerating? _________

15. What is Velocity? Velocity is a measure of the speed of an object AND the direction it is moving in space. On the escalator, passengers are moving at the same constant speed, but they are moving in different directions.  Velocity can change even if speed is remaining constant (you just change direction)   

16. Speed is......._____________________________ Velocity is .... _____________________________

17. Acceleration = the rate of change of velocity Positive acceleration = speeding upNegative acceleration = slowing down Change in Velocity = final velocity (vf) - initial velocity (vi) acceleration (m/s2) =   

18. Change in velocity is often written as  the triangle indicates "change" acceleration = If a car moves at a constant velocity, then its acceleration is zero

19. Calculations A skateboarder is traveling at 8 m/s.  He slows and comes to a stop in 4 sec.  What was the acceleration?  (hint: it is a negative number) What is the Vf?  _____ What is the Vi? _____

20. A sailboat is moving at 12 m/s when a gust of wind changes its velocity to 18 m/s.  The wind lasts 10 seconds.  For that 10 sec, what was its acceleration? A sailboat is moving at 12 m/s when a gust of wind changes its velocity to 18 m/s.  The wind lasts 10 seconds.  For that 10 sec, what was its acceleration? What is the Vf? _______ What is the Vi? _______ What is the t?  _______

21. Think about this....    What are three ways to change the velocity of a car? Accelerate Decelerate Change direction

22. Velocity = displacement/time  If a person is walking at 4 m/s, how far can he travel in 30 seconds? a)  120 meters       b)  7.8 meters       c) .08 meters 2.  A spaceship can move 100 meters in 2 seconds.  What is the ship's velocity? a)  200 m/s              b)  50 m/s            c)  .002  m/s 3.  A chicken runs across the street at a speed of 12 m/s.  If the road is 36 meters across, how long does it take for the chicken to cross the road? a)  3 s         b)  432 s          c)  .333 s

23. QUIZ TIME -  MOTION

24. 1. Motion indicates a change in _____________ 2.  Motion is relative to a ______________________ 3.  Acceleration is a change in ____________ 4.  Speed =  distance /  ? 5. Velocity is a measure of an object's speed and its                      __________________________

25. 6.  The slope of the line on the graph will tell you the object's ______________________.  Hint:  You calculated this for the turtle races. 7.  The triangle in the equation represents ________ 8. If you are slowing down, then you have a ____________ acceleration.

26. EQUATION:  VELOCITY = distance / time 9.  A boat moves 100 meters in  25 seconds.   What is the boat's velocity.  SHOW YOUR WORK by writing the equation with the numbers plugged in. 

27. Instantaneous Velocity • The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero. • The instantaneous velocity indicates what is happening at every point of time.

28. Instantaneous Velocity, graph • The instantaneous velocity is the slope of the line tangent to the x vs. t curve. • This would be the green line. • The light blue lines show that as t gets smaller, they approach the green line.

29. A Note About Slopes • The slope of a graph of physical data represents the ratio of change in the quantity represented on the vertical axis to the change in the quantity represented by the horizontal axis. Section 2.2

30. Instantaneous Velocity, equations • The general equation for instantaneous velocity is: • The instantaneous velocity can be positive, negative, or zero. Section 2.2

31. Instantaneous Speed • The instantaneous speed is the magnitude of the instantaneous velocity. • The instantaneous speed has no direction associated with it. Section 2.2

32. Model: A Particle Under Constant Velocity • Constant velocity indicates the instantaneous velocity at any instant during a time interval is the same as the average velocity during that time interval. vx = vx, avg • The mathematical representation of this situation is the equation. • Common practice is to let ti = 0 and the equation becomes: xf = xi + vx t (for constant vx) Section 2.3

33. Particle Under Constant Velocity, Graph • The graph represents the motion of a particle under constant velocity. • The slope of the graph is the value of the constant velocity. • The y-intercept is xi. Section 2.3

34. Model: A Particle Under Constant Speed • A particle under constant velocity moves with a constant speed along a straight line. • A particle can also move with a constant speed along a curved path. • This can be represented with a model of a particle under constant speed. • The primary equation is the same as for average speed, with the average speed replaced by the constant speed. Section 2.3

35. Average Acceleration • Acceleration is the rate of change of the velocity. • Dimensions are L/T2 • SI units are m/s² • In one dimension, positive and negative can be used to indicate direction. Section 2.4

36. Instantaneous Acceleration • The instantaneous acceleration is the limit of the average acceleration as t approaches 0. • The term acceleration will mean instantaneous acceleration. • If average acceleration is wanted, the word average will be included. Section 2.4

37. Instantaneous Acceleration – graph • The slope of the velocity-time graph is the acceleration. • The green line represents the instantaneous acceleration. • The blue line is the average acceleration. Section 2.4

38. Graphical Comparison • Given the displacement-time graph (a) • The velocity-time graph is found by measuring the slope of the position-time graph at every instant. • The acceleration-time graph is found by measuring the slope of the velocity-time graph at every instant.

39. Acceleration and Velocity, Directions • When an object’s velocity and acceleration are in the same direction, the object is speeding up. • When an object’s velocity and acceleration are in the opposite direction, the object is slowing down.

40. Motion Diagrams • A motion diagram can be formed by imagining the stroboscope photograph of a moving object. • Red arrows represent velocity. • Purple arrows represent acceleration.

41. Constant Velocity • Images are equally spaced. • The car is moving with constant positive velocity (shown by red arrows maintaining the same size). • Acceleration equals zero. Section 2.5

42. Acceleration and Velocity • Images become farther apart as time increases. • Velocity and acceleration are in the same direction. • Acceleration is uniform (violet arrows maintain the same length). • Velocity is increasing (red arrows are getting longer). • This shows positive acceleration and positive velocity.

43. Acceleration and Velocity • Images become closer together as time increases. • Acceleration and velocity are in opposite directions. • Acceleration is uniform (violet arrows maintain the same length). • Velocity is decreasing (red arrows are getting shorter). • Positive velocity and negative acceleration.