1. Simulations
addition_en.html

2. Famous train problems!
A train leaves Provo for SLC at 8:00 am, going 10 mph. A second express train leaves Provo for SLC at 9 am, going 15 mph. It is 40 miles to SLC. Will the 2nd train catch up before SLC? Where?
If someone on the first train looks back and sees the second train getting closer, with what speed does the gap between them narrow? This is the magnitude of the relative velocity (difference in velocities).

3. Concept review
Which of the following graphs represents 1. a bike moving at constant velocity 2. a car speeding up then slowing down 3. a ball thrown up in the air that comes back down 4. a car that always speeds up 5. a motorcycle that slows down and parks. Careful! a, b are velocity v(t), and the others are position x(t)

4. Acceleration Position: where the object is.
Displacement: change in position.
Velocity: rate of change in position with time: instantaneous velocity is slope of x vs t graph.
Acceleration: rate of change in velocity with time

6. Some typical accelerations
Free-fall: 9.8 m/s2
Space shuttle launch: 20 m/s2
Extreme amusement park rides 20 to 50 m/s2 in turns
Fighter pilots: 40 to 80 m/s2 in turns

7. Free-fall acceleration g varies slightly!
Among major cities: Lowest in Mexico City (g = m/s²) Highest in Oslo (g = m/s²) Provo g = m/s2
So we use
g = 9.80 m/s2

8. Air Force’s Dr. John Stapp
In 1954 he rode the "Sonic Wind" at 620 mph (280 m/s), to a dead stop in 1.4 seconds. Max a: 45 g’s.

9. Easier! Easier! Review New What do we mean by +/- acceleration?
What do we mean by +/- position?
being on the + or - side of the origin
What do we mean by +/- velocity?
moving in the + or – direction. Change in position is +/-
New
What do we mean by +/- acceleration?
the change in velocity is in the + or – direction. 
If a is in same direction as v, speeds up
If a is in opposite direction as v , slows down
Easier!
a is in the same direction as the force that causes v to change.
Easier!

10. A car moves left at constant speed. a is ____
Examples of acceleration direction or sign
A car moves left at constant speed. a is ____
A car moving left is slowing down. a is ____
A car moving left speeds up. a is ____
If a is in same direction as v, speeds up
If a is in opposite direction as v , slows down
a is in the same direction as the force that causes v to change.

11. Paddle-bunji-ball
P1. What is the direction of a of the ball while traveling to your right and slowing down because the elastic stretches?
right
left
zero
P2. What is the direction of a when the ball is coming back (to your left, and speeding up)?
P3. What is the direction of a at the instant the ball is stopped by the elastic and about to start coming back?

12. Paddle-bunji-ball
Sketch a(t) for the ball being hit, going to right, and coming back.

13. Ball thrown upward into air
What is the direction of the acceleration…
while throwing:
while it’s traveling up:
at the very top:
while falling down:

14. Ball thrown upward into air
Sketch a(t) for the ball being thrown, going up, and coming back down.

15. “Free-falling” motion
…if an object has only the force of gravity on it, whether going up or down…
acceleration is ______ with direction_________
(have to neglect air friction…OK when v is small )

16. General case of constant a
v(t) graph is a _______________ x(t) graph is a ________________

17. “Kinematic equations” for constant a case
Given on formula sheet for exams

18. b) his average velocity c) his final velocity
A boy runs 50 m, starting at rest, with a constant acceleration of 0.25 m/s2. Find:
a) the time it took
b) his average velocity
c) his final velocity
Draw a diagram!
Label with symbols, numbers for “initial” and “final” cases
Look for connection with equations.

19. A boy runs 50 m, starting at rest, with a constant acceleration of 0
A boy runs 50 m, starting at rest, with a constant acceleration of 0.25 m/s2.
Find:
a) the time it took
b) his average velocity
c) his final velocity

20. Free-fall and kinematic equations
Acceleration due to gravity choose up or down as positive direction, which determines whether g is + or – acceleration. A monkey drops from a tree and takes 2 sec to hit the ground. How far did the monkey drop? What was his average velocity?

21. Given only the information in the diagram, which single kinematic equation can be used to answer the following in one calculation: P5) How long does it take to reach the top of its path? P6) What is the velocity just before it was caught? P7) What was the average velocity for the motion? P8) How long is it in the air?

23. milk drop demo

24. Concept review
Which of the following graphs represents 1. a bike moving at constant velocity 2. a car speeding up then slowing down 3. a ball thrown up in the air that comes back down 4. a car that always speeds up 5. a motorcycle that slows down and parks. Careful! a, b are velocity v(t), and the others are position x(t)

25. Lecture 3, acceleration Basic concepts: Basic problems, skills:
a as slope of v(t)
directions and signs of a, including when objects stop and reverse
Basic problems, skills:
single step using a kinematic equation
drawing good diagrams, using symbols
Advanced problems, skills:
more than one step using kinematic equations
using quadratic equation to find t, or using two kin. eqns.
using two different a’s in one problem