Describing Motion

1. Describing Motion

2. Motion Diagrams • Imagine a strobe light illuminating a runner- you would see their motion in a series of “frozen” positions • Motion (or ticker tape) diagrams show series of images taken at equal time intervals • Imagine the track of a car that spills a drop of oil every second

3. Motion Diagrams

4. Motion Diagrams

5. Check your understanding: Draw a motion diagram for the following scenarios: Constant speed Acceleration Deceleration

6. Particle Model • You’ll notice that our motion diagrams were dots- not runners or cars or planes • We make assumptions sometimes to simplify- in motion we assume that the entire object is a particle located at the center of mass

7. Where? Coordinate Systems • Coordinate system tells you the origin and direction of motion • Origin- values=0 (the starting point) • We use the x,y,z axes so there is both a distance and direction to measurements of motion • The vector shows the magnitude and direction

8. Scalar Tells only magnitude Ex: Kaneohe is 14 miles from Pearl Harbor Vector Tells magnitude and direction Ex: Kaneohe is 14 miles ENE from Pear Harbor Usually put an arrow over to denote vector- ie velocity is v Scalar and Vector Quantities

9. Scalar and Vector • Divide the following into scalar and vector quantities • Time • Temperature • Displacement • Mass • Velocity

10. Vector Quantities and Direction • Using our coordinate system, vector quantities can be negative • Ex: if you move left from the origin along the x axis, the convention is to make this negative

11. And now for some Greek In physics we use a lot of Greek letters as symbols!

12. Our Friend,  •  is used to show a change in a quantity • We say “delta” or “change in”

13. Time Interval • In measuring motion, we often need the time interval- how long it took from start to finish • Time interval= t • t=t1-t0

14. Displacement and Distance • Displacement is change in position of an object • Is it scalar or vector? • VECTOR- it has direction • The magnitude of the displacement is called distance so it is SCALAR

15. Now you try- what is the displacement? distance? Displacement is 140m to the right. Distance is 420m.

16. Hmm…try one more • What is the displacement and distance of the cross country team if they run out 10km, turn around and come back to school? • Displacement=0km • Distance=20km

17. Displacement and Distance • d=position • d=displacement=d1-d0 • We draw the displacementvector with the tail at the original position and the tip of the arrow at the ending position

18. Position-Time Graphs • Plot displacement vs time • helps estimate position in between data points • Slope=velocity • slope=speed

19. Examples • P. 39 example 1 • P. 41 example 2

20. Practice Problems • P. 39 #9-11 • P. 41 # 14-17 • When you are done: go to the physics lab online • http://dev.physicslab.org/Document.aspx?doctype=5&filename=Kinematics_ConstantVelocityPositionTimeGraphs1.xml

21. Who is at rest? Traveling slowly in + direction, traveling quickly in negative direction? Traveling quickly in + direction? http://dev.physicslab.org/Document.aspx?doctype=5&filename=Kinematics_ConstantVelocityPositionTimeGraphs1.xml

22. Velocity is vector Speed is scalar Velocity and Speed Can be instantaneous or average- the speedometer of a car gives you instantaneous but over the course of a trip from home to school you will travel at various speeds and even stop sometimes but you will have an average velocity.

23. Average Velocity • Average velocity is the total displacement divided by the total time • v= d/ t • The line over the v means average • We often use the word “per” in our answers as in meters per second- this means the units are m/s

24. Average velocity in graphs • Remember the slope of a position-time graph shows the velocity • Slope=rise over run • v=d1-d2/t1-t0 • Units will be m/s

25. Average velocity in graphs • Since velocity is a vector, it has a direction • If the slope is negative, velocity will be negative

26. Average Speed • Remember, speed is scalar so does not take direction into account • Average speed= total distance over time • Can’t be negative! • Why do we need both speed and velocity? Sometimes we need to know direction and sometimes just the magnitude will do.

27. Example • P. 45 example 3 • Practice problems 25-28 • Note- if travel is in a straight line, average speed= the absolute value of average velocity because distance= absolute value of displacement

28. Using equations • You can describe a straight line using the equation y=mx+b • y=displacement=d • m=slope=velocity=v • x=time=t • b=y intercept=initial position=d0 • d=vt+d0

29. Instantaneous Velocity • Speed and direction of an object at an instant in time • Think of a skateboarder at the top of the ramp- his instantaneous velocity=0 • His average velocity as he skates down the ramp is much more!

30. Pendulum mini-lab p. 46 • Describe: • Motion • Speed • direction • Draw a diagram showing the instantaneous velocity vectors at the top, the midpoint of the way down, the bottom, the midpoint of the way up and the top • Remember vectors are arrows pointing in direction of motion and length is proportional to magnitude • Where was v greatest? Least? • What is the average speed?