Transcript Linear Motion

Linear Motion
Chapter 2
Review time!
• Remember when we were using math in
physics….
Vectors vs Scalars
• Scalars are quantities that have a _______,
or numeric value which represents a size
Examples of these are:_______________
• Vectors are quantities which have a
___________ and a ______, Examples of
these are:_______________
Measuring how fast you are
going
• Speedv
• Scalar
• Standard unit is m/s
distance d
v

time
t
• Velocityv
• Vector
• Standard unit is m/s,
plus direction
displaceme nt d
v

time
t
Velocity and Speed
• If it take the person 4
seconds to walk around
the square, what is her
average speed and
average velocity?
• For speed, d=12m
and t=4s, so v=3m/s
• For velocity, d=0
and t=4s, so v=0m/s
Practice Problem
• A boy takes a road trip from Philadelphia
to Pittsburgh. The distance between the
two cities is 300km. He travels the first
100km at a speed of 35m/s and the last
200km at 40m/s. What is his average
speed?
st
1
step. ID important info
• A boy takes a road trip from Philadelphia
to Pittsburgh. The distance between the
two cities is 300km. He travels the first
100km at a speed of 35m/s and the last
200km at 40m/s. What is his average
speed?
Different types of velocity and
speed
• Average velocity/speed
• A value summarizing
the average of the
entire trip.
• All that’s needed is total
displacement/distance
and total time.
• Instantaneous velocity
• A value that
summarizes the velocity
or speed of something
at a given instant in
time.
• What the speedometer
in your car reads.
• Can change from
moment to moment.
What are we looking for
• Although we are
looking for average
speed…we first
need to find time.
d
V 
t
100
35 
t
t  2.86hr
d
V 
t
200
40 
t
t  5hr
Total time 7.86 hr
Using the total time, you can calculate an
average velocity 38.17 k m
hr
Acceleration
v v f  vi
a  acceleration 

t
t
• delta.
• Means “change in”
and is calculated by
subtracting the initial
value from the final
value.
• Change in velocity
over time.
• Either hitting the gas
or hitting the break
counts as
acceleration.
• Units are m/s2
Acceleration
(vector)
The rate of change in velocity.
-Accelerations cannot happen with out the presence of a
force (a push or a pull)
-Acceleration will depend on the direction of this force
-Constant acceleration is when, in a given amount of time,
acceleration does not change
acceleration
force
force
acceleration
Acceleration
(continued)
Positive acceleration is caused by a force in the positive
direction.
-Depending on the initial movement of an object, a positive
acceleration will either speed up or slow down an object.
- if the object starts at rest or is already moving positively, it
will speed up.
-If the object is moving in the negative direction, a positive
acceleration will slow the object down.
Acceleration
(continued)
Negative acceleration is caused by a force in the Negative
direction.
-Depending on the initial movement of an object, a negative
acceleration will either speed up or slow down an object.
- if the object starts at rest or is already moving negatively, it
will speed up.
-If the object is moving in the positive direction, a negative
acceleration will slow the object down.
Rules for using linear motion
equations
• We always assume that acceleration is
constant.
• We use vector quantities, not scalar
quantities.
• We always use instantaneous velocities, not
average velocities
• Direction of a vector is indicated by sign.
Incorrect use of signs will result in incorrect
answers.
Practice Problem
A car going 15m/s accelerates at 5m/s2
for 3.8s. How fast is it going at the end
of the acceleration?
First step is identifying the variables in
the equation and listing them.
Practice Problem
A car going 15m/s accelerates at 5m/s2
for 3.8s. How fast is it going at the end
of the acceleration?
t=3.8s
vi=15m/s
a=5m/s2
vf=?
Practice Problem 2
• A penguin slides down a glacier starting
from rest, and accelerates at a rate of
7.6m/s2. If it reaches the bottom of the
hill going 15m/s, how long does it take
to get to the bottom?
Practice Problem 2
• A penguin slides down a glacier starting
from rest, and accelerates at a rate of
7.6m/s2. If it reaches the bottom of the
hill going 15m/s, how long does it take
to get to the bottom?
Equation for displacement
d
v
t
Two versions of the
same average velocity
equations
d  vt

v v 
v
i
f
2

v v 
d
t
i
f
2
One more way to
calculate average velocity
Although this equation is not
used often, it is important to
derive other useful equations!
Equation that doesn’t require vf

v v 
d
i
f
2
t
Combine
v f  vi  at

vi  vi  at 
d
t
2
1
d  t (2vi  at )
2
1 2
d  vi t  at
2
Practice Problems
A ball rolling up a hill accelerates at –5.6m/s2
for 6.3s. If it is rolling at 50m/s initially, how far
has it rolled?
If a car accelerates at a rate of 4.64m/s2 and it
travels 162m in 3s, how fast was it going
initially?
An equation not needing t
v f  vi  at
d
1
vi  v f t
2
v f  vi  at
v f  vi
a
t
Combine
 v f  vi 
1

v  v f 
d
2 i
 a 
 v 2f  vi2 

d1 
2 a 


v  v  2ad
2
f
2
i
v  v  2ad
2
f
2
i
A bowling ball is thrown at a speed of
6.8m/s. By the time it hits the pins 63m
away, it is going 5.2m/s. What is the
acceleration?
The Big 3
v f  vi  at
1 2
d  vi t  at
2
v  v  2ad
2
f
2
i
Problem Solving Steps
• Draw a quick sketch
• Identify givens in a problem and write them
down.
• Determine what is being asked for and write
down with a questions mark.
• Select an equation that uses the variables
(known and unknown) you are dealing with
and nothing else.
• Solve the selected equation for the unknown.
• Fill in the known values and solve equation
• Make a chart like this one…if its helpful
Gravity
• Gravity causes an acceleration.
• All objects have the same acceleration due
to gravity.
• Differences in falling speed/acceleration
are due to air resistance, not differences in
gravity.
• g=9.8m/s2 down
• When analyzing a falling object, consider
final velocity before the object hits the
ground and initial velocity the instant the
object is dropped
Hidden Variables
• Objects falling through space can be
assumed to accelerate at a rate of
9.8m/s2 down.
• Starting from rest corresponds to a vi=0
• Coming to a stop corresponds with a vf=0
• A change in direction indicates that at
some point v=0.
• Dropped objects have no initial velocity.
Practice Problem
• A ball is dropped and hits the ground
with a velocity of at a speed of 25m/s.
How far has it traveled when it reaches
the ground?
vi=0 m/s
d=?
vf=25 m/s
t=?
a=g=9.8m/s2
A plane slows on a runway from 207km/hr
to 35km/hr in about 5.27km.
a. What is its acceleration?
b. How long does it take?
An onion falls off an 84m high cliff. How
long does it take him to hit the ground?
An onion is thrown off of the same cliff at
9.5m/s straight up. How long does it take
him to hit the ground?
A train engineer notices a cow on the
track when he is going 40.7m/s. If he can
decelerate at a rate of -1.4m/s2 and the
cow is 500m away, will he be able to stop
in time to avoid hitting the cow?
Practice Problems
• A car slows from 45 m/s to 30m/s over
6.2s. How far does it travel in that time?
• A cyclist speeds up from his 8.45m/s
pace. As he accelerates, he goes 325m
in 30s. What is his final velocity?