1. KINEMATICS IN ONE DIMENSION
CHAPTER 2
GIANCOLI

2. MECHANICS
THE STUDY OF MOTION OF OBJECTS AND THE RELATED CONCEPTS OF FORCE AND ENERGY
DIVIDED INTO TWO PARTS

3. KINEMATICS
HOW OBJECTS MOVE

4. DYNAMICS
WHY OBJECTS MOVE

5. TRANSLATIONAL MOTION
MOTION WITHOUT ROTATION

6. FRAME OF REFERENCE
ANY MEASUREMENT OF POSITION, VELOCITY, OR DISTANCE MUST HAVE A POINT OF REFERENCE.
COORDINATE AXES
DISPLACEMENT – CHANGE IN POSITION

7. AVERAGE VELOCITY AVERAGE SPEED = DISTANCE/TIME
AVERAGE VELOCITY=DISPLACEMENT
TIME

8. SCALAR V.S. VECTOR SCALAR – MAGNETUDE ONLY
VECTOR – MAGNETUDE + DIRECTION

9. WHITE BOARD ACTIVITY
THE POSITON OF A RUNNER AS A FUNCTION OF TIME IS PLOTTED AS MOVING ALONG THE X AXIS OF THE COORDINATE SYSTEM. DURING A 3.00 S TIME INTERVAL, THE RUNNER’S POSITON CHANGES FROM 50.0M TO 30.5M. WHAT IS THE RUNNER’S AVERAGE VELOCITY?

10. MOTION OF RUNNER
GRAPH OF RUNNER X X

11. ANSWER
-6.50 M/S
WHY IS IT NEGATIVE?

12. PRACTICE
HOW FAR CAN A CYCLIST TRAVEL IN 2.5 H ALONG A STRAIGHT ROAD IF HER AVERAGE SPEED IS 18 KM/H?
45 KM

13. INSTANTANEOUS VELOCITY
THE AVERAGE VELOCITY OVER AN INFINTESIMALLY SHORT TIME.
WHY DOES INSTANTANEOUS SPEED ALWAYS EQUAL INSTANTEOUS VELOCITY?
BECAUSE DISTANCE AND DISPLACEMENT BECOME THE SAME WHEN THEY ARE INFINTESIMALLY SMALL.

14. ACCELERATION
THE RATE OF CHANGE OF THE VELOCITY OVER A GIVEN PERIOD OF TIME.
AVERAGE ACCELERATION IS THE CHANGE IN THE VELOCITY DIVIDED BY THE TIME TAKEN TO MAKE THIS CHANGE.

15. PRACTICE
A CAR ACCELERATES ALONG A STRAIGHT RAOD FROM REST TO 75 KM/H IN 5.0 S. WHA TIS THE MAGNITUDE OF ITS AVERAGE ACCELERATION?
15 KM/H/S

16. QUESTION
IF THE VELOCITY OF AN OBJECT IS ZERO, DOES IT MEAN THAT THE ACCELERATION IS ZERO?
IF THE ACCELERATION IS ZERO, DOES THAT MEAN THE VELCITY IS ZERO?

17. UNIFORMLY ACCELERATED MOTION
CONSTANT ACCELERATION
THE MAGNETUDE DOES NOT CHANGE
THE DIRECTION DOES NOT CHANGE

18. CONSTANT ACCELERATION EQUATIONS
V=Vo + AT
X = Xo + VoT + 1/2AT2
V2 = Vo2 +2A(X-Xo)
V = V + Vo 2

19. PROBLEM SOLVING RECIPE
READ AND REREAD
DRAW A DIAGRAM
WRITE DOWN KNOWNS
THINK…WHAT PRINCIPLES APPLY
EQUATION/S NEEDED
CALCULATIONS
DOES YOUR ANSWER SEEM REASONABLE?
CHECK YOUR UNITS. THIS CAN SERVE AS A FAILSAFE FOR YOU.

20. FALLING OBJECTS PRIME EXAMPLE OF UNIFORMLY ACCELERATED MOTION
ACCELERATION IS DUE TO GRAVITY
9.80 m/s/s

21. GALILEO’S HYPOTHESIS ..FREE FALL IS AT CONSTANT ACCELERATION G.
…SUMMARIZE GALILEO’S CONTRIBUTION….AT A GIVEN LOCATION ON THE EARTH AND IN THE ABSENCE OF AIR RESISTANCE ALL OBJECTS FALL WITH THE SAME CONSTANT ACCELERATION.
IT APPROXIMATE MAGNETUDE IS 9.80 M/S/S

22. PROBLEM
SUPPOSE THAT A BALL IS DROPPED FROM A TOWER 70.0 M HIGH. HOW FAR WILL IT HAVE FALLEN AFTER 1.00S, 2.00S, AND 3.00S? ASSUME Y IS POSITIVE DOWNWARD. NEGLECT AIR RESISTANCE.

23. ANSWER
Y=1/2AT2
4.90 M
19.6 M
44.1 M

24. PRACTICE MORE
WHAT IF THE BALL IS THROWN DOWNWARD WITH AN INITIAL VELOCITY OF 3.00 M/S, INSTEAD OF BEING DROPPED.
A. WHAT THEN WOULD BE ITS POSTION AFTER 1.00S, 2.00S?

25. ANSWER
X = Xo + VoT + 1/2AT2
Y = VoT + 1/2AT2
7.90 M
25.6 M

26. MORE WHAT WOULD ITS SPEED BE AFTER 1.00S AND 2.00S? V=Vo + AT 12.8 M/S
NOW CALCULATE THE SPEEDS OF THE DROPPED BALL FOR 1.00 S AND 2.00 S.

27. MORE
9.80 M/S
19.6 M/S
HOW DO THESE SPEEDS COMPARE TO THE SPEEDS OF THE DROPPED BALL?
THE SPEED OF THE BALL INCREASES LINEARLY WITH TIME FOR BOTH SCENERIOS, BUT THE THROWN BALL IS ALWAYS 3.0 M/S GREATER THAN THE BALL IN FREE FALL.

28. OBJECTS THROWN UPWARD
WHAT GOES UP MUST COME DOWN IN THE SAME AMOUNT OF TIME IT TOOK TO GO UP!
ACCELERATION IS G GOING UP AND DOWN
V = 0 M/S AT THE ZENITH
WHAT IS THE ACCELERATION AT THE ZENITH?

29. QUESTIONS ARE VELOCITY AND ACCELERATION ALWAYS IN THE SAME DIRECTION?
WHAT IS THE ACCELERATION OF AN OBJECT AT ITS HIGHEST POINT?

30. QUADRATIC FORMULA
THERE MAY BE TIMES YOU WILL NEED TO USE THE QUADRATIC FORMULA IN PROBLEM SOLVING. SEE EXAMPLE 2-15 ON PAGE 37 FOR A CLEAR AND CONCISE EXAMPLE.

31. GRAPHICAL ANALYSIS OF LINEAR MOTION
SLOPE ON A POSITION/TIME GRAPH IS EQUAL TO THE VELOCITY
SLOPE ON A VELOCITY/TIME GRAPH IS EQUAL TO ACCELERATION.
THE AREA UNDER THE CURVE IN A VELOCITY/TIME GRAPH IS EQUAL TO THE DISPLACEMENT