2. CCHS Physics Introduction to and VELOCITY

3. Outline Vector vs. Scalar Displacement vs. Distance Speed vs. Velocity Instantaneous vs. Average Factor Label Method

4. Side Note Mechanics = the study of motion Start with Kinematics –Study of motion without regard to why Overall study is Dynamics –Explores the effect that forces have on motion Chapter 1 goes over units of measure: –3 fundamental quantities length, mass, time –Not going to go over this (however you are responsible for the material)

5. Vector vs. Scalar Scalar: –has only magnitude (size) Vector: –Has magnitude and direction

6. Displacement vs. Distance Displacement: –Change in position, the difference between the final and initial coordinates (vector) –  x = x f - x o –For the beginning we will deal with 1D motion, designate direction with + / - sign Distance: –The total length you have traveled (scalar)

7. Disp vs Dist cont. Need to distinguish how long we traveled from how far away (and in what direction) we traveled START FINISH

8. Positive and Negative Displacements

9. Displacement Movie

10. Disp vs Dist cont Example 1 –Hit a home run Dist = 360 ft, disp = 0 ft Example 2 –Walk to a friends house 2 mi west and then go 1/2 mi east Disp = 1.5 mi west, dist = 2.5 mi Example 3 –Drive 30 mi north then 40 mi west Disp = 50 mi @ 67° W of N, dist = 70 mi

11. Average Speed and Velocity

12. Average Speed and Velocity cont. Example 1 –Reverse at 5 mph Speed = 5 mph, velocity = -5 mph Speedometer reads speed Example 2 –Run around 400 m track in 60 s

13. Instantaneous vs. Average The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.

14. Velocity Sign Convention

15. Factor Label Method (Also known as Dimensional Analysis) Use this to convert between different units Multiply by unity so that units cancel on the diagonal. Example: Convert 75 mph to m/s.

16. Time to “Learn” Calculus Derivative: the rate of change of one variable with respect to another –Equivalent to finding the slope –Symbol: Derivative Dragon

17. Mathematical Example Mathematical Procedure: –There is a formal procedure that you will learn in math. –I will show you the trick by an example You try, find dy/dx of y = 2x 4

18. Few More Examples Find dy/dx of y = 3x 3 Find dy/dx of y = 2x Find dy/dx of y = 14 Find dy/dx of y = 6x 8 +4x 2

19. Instantaneous Velocity We know that instantaneous velocity is the change in position at a given instant in time. This is perfect for the use of derivatives!

20. Relation to Physics So, rate of change of position with respect to time (the derivative) is velocity –v is the rate at which the particle’s position x is changing with time at a given instant EXAMPLE: If the position of an car is given by the equation x(t)=3t 2 +5, find the velocity at 4 s.

21. More Calculus, Learning Part II Integral: The sum of a series of multiplications –Equivalent to finding the area under a curve –Symbol: –Basically, this is the opposite to integrating –Derivatives and Integrals are inverse operations

22. Mathematical Example Mathematical Procedure: You try, find Check:

23. Few More Examples, Again Find

24. Relation to Physics We all know the equation, d=rt. So, if you are going 5 m/s for 3 s, you go 15 m/s. BUT … what if the velocity isn’t constant, what then? HAVE NO FEAR, INTEGRAL MAN IS HERE!!!!! INTEGRAL MAN

25. Example If the velocity of your car is given by v(t)=3t+4. How far have you gone after 6 s?