Simulations http://phet.colorado.edu/en/simulation/moving-man http://phet.colorado.edu/sims/vector-addition/vector- addition_en.html

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).

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)

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

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

Free-fall acceleration g varies slightly! Among major cities: Lowest in Mexico City (g = 9.779 m/s²) Highest in Oslo (g = 9.819 m/s²) Provo g = 9.799 m/s2 So we use g = 9.80 m/s2

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.

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!

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.

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?

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

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:

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

“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 )

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

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

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.

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  

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?

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?

milk drop demo

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)

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