1. Describing Motion: Kinematics in One Dimension
Sept 9: Chapter 2
Describing Motion: Kinematics in One Dimension
Review the quiz?
Warning: former students say kinematics is hard at first………..but by December they say it is easy

2. First, a question
You walk at 0.80 m/s through the woods. How long will it take for you to travel km?
Report in seconds.
Report in hours.
Manage sig figs.

3. Managing homework If you don’t have 75% of your assignment done…
Give yourself a HW check
Write date, name, and assignment you missed in “the purple notebook”
If, two classes later, you haven’t done it, you’ll get one more HW check

4. Sections of Chapter 2 we will cover…
Reference Frames and Displacement
Average Velocity
Instantaneous Velocity
Acceleration
Motion at Constant Acceleration
Solving Problems
Falling Objects
Graphical Analysis of Linear Motion

5. Speed of the bowling ball
Using only what you have, estimate the speed as I roll it.
What is the velocity?
It is 100,000 km/hr! Yes, it is.
What is the acceleration?
We need to define our reference for measurement.

6. 2-1 Reference Frames
Any measurement of position, distance, or speed must be made with respect to a reference frame.
For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher.

7. 2-1 Displacement
We make a distinction between distance and displacement.
Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.
Distance traveled (dashed line) is measured along the actual path taken.
We will use both.

8. 2-1 Displacement The displacement is written: Left:
Displacement is positive.
Right:
Displacement is negative.

9. 2-2 Average Speed & Velocity
Speed: how far an object travels in a given time interval
(2-1)
Velocity includes directional information:
Check: *can avg speed be lower than avg velocity?
* What is slowest avg speed? Highest? …

10. check
Yesterday, this book was at my desk, and today it is here. Calculate average v.
North America drifts about 1 inch per year.
What is average velocity in SI units?

11. 2-3 Instantaneous Velocity
The instantaneous velocity is like the average velocity, in the limit as the time interval becomes infinitesimally short.
(2-3)
These graphs show (a) constant velocity and (b) varying velocity.
Check: graph my acceleration.

12. Velocity with go-motion
Observe this cart motion and estimate the instantaneous velocity in SI units.
Now check it with go-motion device.

13. Let’s talk graphs and carts
A car on a track, x is position from origin
What is positive, what is negative?
Now you Plot x vs. t, identify origin (0,0)
X is plotted on vertical but represents horizontal !?!?
What does slope tell us?
What is velocity, what does it look like?
Think about physical motion, and think about graphical representation of that motion.
Check: given constant velocity, what is a?

14. Make graphs from motion
bowling ball on ground
Fan car on ground
Fan car up a sloped table, no motion
Bowling ball down sloped table
Bowling ball up a sloped table

15. a b x x t t c d x v t t

16. Take the motion graph challenge on loggerpro
Loggerpro FILE/OPEN/Physics/graphmatching 1b 1c 1d
1e velocity
1g velocity

17. *2-4 Acceleration
Acceleration is the rate of change of velocity. (How fast is velocity changing)

18. 2-4 Acceleration
Acceleration, like velocity is a vector, although in one-dimensional motion we only need the sign.
The previous image shows positive acceleration; here is negative acceleration with positive velocity:

19. 2-4 more Acceleration
There is a difference between negative acceleration and deceleration:
Negative acceleration is acceleration in the negative direction as defined by the coordinate system.
Deceleration occurs only the acceleration is opposite in direction to the velocity.
I recommend avoiding the term deceleration in this class.

20. 2-4 Acceleration
The instantaneous acceleration is the average acceleration, in the limit as the time interval becomes infinitesimally short.
(2-5)
It is a snapshot of the acceleration at a given moment.
Check: graph my acceleration…

21. Acceleration check
A car drives 25m/s and then accelerates to 45m/s in 10.0 seconds.
What is average acceleration?
In the morning, I drive my car from our garage to the school and park. My maximum speed is 45mph and the trip takes me 10 minutes. What is average acceleration of my car?

22. Special case: Motion at Constant Acceleration (the math that works for us)
We can write the average velocity of an object during a time interval t as
The acceleration, now assumed or known to be constant, is
What do these all mean?
Check: estimate the a for this motion…

23. 2-5 Motion at Constant Acceleration, deriving the useful equations.
In addition, as the velocity is increasing at a constant rate, we know that the average is:
Combining these last three equations, we find:
(2-8)
(2-9)
Note: I will not expect you to derive these kinematic equations…

24. 2-5 Motion at Constant Acceleration, the kinematic equations
We can also combine these equations so as to eliminate t:
We now have all the equations we need to solve constant-acceleration problems.
(2-10)
(2-11a)
(2-11b)
(2-11c)
(2-11d)

25. A typical (classic) problem
You push gently on the accelerator of your brand new car, and the car moves from a stop to 22m/s in 63 m. Find a.
Draw at beginning and at end = 2 pictures
What do you know at each time?
What equation will use this info and give you a?
Solve symbolically for a and check units.
Now calculate the number and sig figs.
Does your answer make sense?

26. *“The Big 7” Problem solving steps
Draw and label the situation at two times
Write something for xo, x, to, t, vo, v, and a
Decide and show which direction is +
Find the correct kinematic equation
Delete what is zero
Solve algebra for desired unknown (do one unknown at a time)
Check the units of the algebraic equation
Plug in the numbers and units, calculate.
Fix answer for correct sig figs

27. 2-6 Solving Problems (Big 7 are in red)
Read the whole problem and make sure you understand it. Then read it again.
Decide on the objects under study and what the time interval is.
Draw a diagram and choose coordinate axes.
Write down the known (given) quantities, and then the unknown ones that you need to find.
What physics applies here? Plan an approach to a solution.

28. 2-6 Solving Problems (cont)
6. Which equations relate the known and unknown quantities? Are they valid in this situation? Solve algebraically for the unknown quantities, and check that your result is sensible (correct dimensions).
7. Calculate the solution and round it to the appropriate number of significant figures.
8. Look at the result – is it reasonable? Does it agree with a rough estimate?
9. Check the units again.

29. Constant acceleration
It is one number
It is one value
It can be zero
What are examples?

30. Demo with fan car and GoMotion
Measure x, v, a
Calculate a and check it

31. 2-7 Falling Objects
Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity.
This is one of the most common examples of motion with constant acceleration.
We love it.

32. 2-7 Falling Objects
In the absence of air resistance, all objects fall with the same acceleration, although this may be hard to tell by testing in an environment where there is air resistance.

33. Demo: book and paper, vacuum and feather
Sketch the set up and show me
Write the procedure in 4-5 bullet points
write these answers
What happens to the air in the chamber?
Why do paper and feather fall slowly?
Why does magnet fall quickly?
Why does feather fall slower than paper?
Why do meteorites burn up in the atmosphere?
Can anything fall in air without any friction?

34. 2-7 Falling Objects, the data
The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s2.

35. How to solve vertical motion kinematics?
Same as horizontal!
And know that a = -g when up is positive

36. Look at HW problems Practice together Do example 2-5
And do p-27 together in class

37. 15 sept: More on graphs Plots of x vs. t or v vs. t
Look at 6 cases on next page
Describe motion of each
Derive companion graphs from each
Always do graph down first
Add numbers if it helps
Be sure you can understand units of each

38. x v a t x v a t x v a t
The important 6 graphs x v a t x v a t x v a t

39. Quiz on motion
A fan car has constant acceleration from 4.0m/s to 1.0 m/s in 2.0 m.
What is a?
What is tf?
Plot the motion graphs x, v, and a without numbers

40. Understanding x, v, and a
To understand motion, we need to understand the graphs of x, v, and a vs. t, and know how those relate to actual motion.
Check
X,v,a, of no motion, constant position
Xva of constant velocity
Xva of constant acceleration

41. *Check your “graphs understanding”
Draw x,v,a vs. t for each motion
Motions:
fan car push away
Ball toss up
Ball bounce
Falling coffee filter x v a t

42. Now make it real
Write each of these motion graphs on a page you can carry.
Go into the hall and practice each motion as a table, reach consensus.
I will quiz you in 5 minutes using Loggerpro and this cart.
Each group will match the graph on Loggerpro

43. 2-8 Graphical Analysis of Linear Motion
You’ve done this in math?
This is a graph of x vs. t for an object moving with constant velocity. The velocity is the slope of the x-t curve.

44. Graphical analysis made easy
6m/s
Area under the v-t curve = the distance traveled v t 5s
How far did this object go in 5s?
What is the area under this curve?
The same is true for any shape of v-t curve!

45. 2-8 Graphical Analysis of Linear Motion
On the left we have a graph of velocity vs. time for an object with varying velocity; on the right we have the resulting x vs. t curve. The instantaneous velocity is tangent to the curve at each point.

46. 2-8 Graphical Analysis of Linear Motion
Don’t need this yet!
The displacement, x, is the area beneath the v vs. t curve.

47. Quiz on a classic problem
I stand on the school roof and drop a rock from 6.0 m.
Draw a picture.
Write in all known and unknown values for t, y, v, and a.
How long does it take to hit the ground?
How fast is it going when it hits?

48. Summary of Chapter 2
Kinematics is the description of how objects move with respect to a defined reference frame.
Displacement is the change in position of an object.
Average speed is the distance traveled divided by the time it took; average velocity is the displacement divided by the time.
Instantaneous velocity is the limit as the time becomes infinitesimally short.

49. Summary of Chapter 2 cont.
Average acceleration is the change in velocity divided by the time.
Instantaneous acceleration is the limit as the time interval becomes infinitesimally small.
The equations of motion for constant acceleration are given in the text; there are four, each one of which requires a different set of quantities.
Objects falling (or having been projected) near the surface of the Earth experience a gravitational acceleration of 9.80 m/s2.
We can solve problems using 7 steps…

50. Practice during single sessions: 16 P 26 and 57

51. Classics chapter 2 Simple horizontal acceleration; fan car
Ball off a cliff, with v0 = 0 (use newton ball to demo)
Ball off a cliff, but with initial velocity down
Ball thrown up and falls down
Car braking to a stop, how far, or time
Car into tree, front compresses, what is a?
Guy falls into net, decelerates, two parts
The 6 graphs of x, v, a vs t

52. Comments on exam 1
Physics (and Chem) are often the first classes where some students get grades less than 90%. Was true for me.
Don’t panic on this test.
You have seen all the techniques: algebra, vectors, solving problems
You just need practice.
You can do this.

53. Exam 1 post mortem Review with different pen Record correct answers
Mean = average = 89%
Low=60; high = 100
Review with different pen
Record correct answers
Let me know after class if addition or correction mistake by me
Take exam and correct any answer for Friday. Make this legible. Attach sheet to show new work.

54. Lab 1: velocity and acceleration of a bowling ball
3 per group.
Share a ball to get set up.
Find or build a ramp.
5 min: agree on plan, assign tasks
5 min: set up and take a trial run with timers
15 min: conduct runs with GoMotion and timers
10 min: short present to Dr. F of results. Save data
5 min: clean up

55. TC marathon