Transcript Velocity - BYU Physics and Astronomy

Simulations
http://phet.colorado.edu/en/simulation/moving-man
http://phet.colorado.edu/sims/vector-addition/vectoraddition_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
aavg
v


t
a (t )  slope of v(t ) graph
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.
Review
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
 a is in the same direction as the force that causes v to
change.

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?
A. right
B. left
C. 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
v f  vi  at
vav 
v f  vi 

 or a 

t 

v f  vi
2
x  vav t
1 2
x  vi t  at
2
v f 2  vi 2  2ax
Given on formula sheet for exams
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 0.25 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?
A. v f  vi  at
B. vav 
v f  vi
2
1 2
C. y  vi t  at
2
D. v f 2  vi 2  2ay
E. More than one equ. is needed
milk drop demo
v 
y
t
v
a 
t
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:
◦ 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