Kinematics in One Dimension - Bibb County Schools

doutfanaticalMechanics

Nov 14, 2013 (3 years and 1 month ago)

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Fill in the missing bubble…

Kinematics in One
Dimension

Chapter 2

Kin
-
e
-
what?


Kinematics



the branch of
_________

which
describes the motion of an object without
explicit reference to the ______ that act on the
object.


Mechanics



the branch of Physics that deals
with the ______ of objects and the ______ that
change it.


One Dimension



dealing only with ________
motion.

mechanics

forces

motion

forces

linear

Familiar terms?


Can you define the following? Take a minute
to write down your answer, then, using the
same groups for the poster, votefor the

best


choice. DO NOT look in in your book!


Displacement


Velocity


Acceleration


Alright, let

s share…

So what do they really mean?

SP1. a1Determine the difference between
distnace and displacement

SP1.a2 Identify the displacement, time and
velocity [s, t, v]


Displacement

(s) is similar to distance. It is, in
general, the change in position of an object.


Answers the question

How far

.


Distance

is the total amount from the beginning
of travel


Displacement

is always measured from the
origin to the current position.


Student walking around demo!!

So what do they really mean?

SP1.a4 Describe the difference between speed
and velocity [speed, v
avg
]


Velocity

(v
avg
) is similar to _________ (again,
difference later). It is defined as the change in
displacement divided by time.


Answers the question

How Fast



Speed does not care about direction


Velocity changes as direction changes


Can you write the equation?


speed

So what do they really mean?

SP1.a3 Calculate the velocity of an object.
[v=s/t]


That equation would be






This is called a definition equation. You will
use it to derive other equations in this course.


Do you see what the units would be?

v


s

t
So what do they really mean?

SP1.a6 Calculate the acceleration of an object.


Acceleration

(a) is the change in ________ of
an object divided by the time interval.


You must do one of 3 things:


Increase velocity


Decrease velocity


Change direction


If there is no speed change or direction change,
there is NO ACCELERATION.


Can you write the equation?

velocity

So what do they really mean?


Did you get






Again, another definition equation.


Special Note: Very rarely does time NOT
begin at zero. Therefore, it is very common to
write these equations without the
Δ

symbol by
time.

a


v

t
Looking deeper at Displacement

Can you answer the following questions?

(avoid using your calculator)

1.
A student walks 15 m from the commons,
stops at her locker, then continues 20 m to
her classroom. What is her displacement?

2.
Another student walks 30 m from the
commons before realizing he meant to stop at
his locker. He returns 10 m to his locker,
then turns back toward his class, 20 m from
his locker. What is his displacement?

35 m

40 m

Looking Deeper at Displacement

SP1.b1 Describe and identiy scalar and vector
quantities


So what makes the difference between 60 m or
40 m for question #2?


The difference is that 60 m is the
distance

the
student travels (a ______ qty), but 40 m is the
displacement

(a ______ qty).


Vectors take into account the direction of
motion. In #2 there was a change of direction.
Mathematically, this is a change in sign for the
number. So… 30 m + (
-
10 m) + 20 m

scalar

vector

Looking Deeper at Velocity


Okay, explanation first this time.
Speed is the
scalar qty for velocity. So, speed is magnitude
only (just a number). Velocity is magnitude
and

direction.


Two other terms to note:

___________ Velocity = v right now

_______ Velocity = overall v: (v = (v
f

+ v
i
)/2)


Remember, a + or


count as direction. You
do not have to say north, south, toward, away,
etc., but you may see them in a question.


Instantaneous

Average

Looking Deeper at Velocity

Alright, try these two questions on for size:

1.
A driver traveling north on I
-
85 notes that it
takes 2 minutes to get from exit 99 to exit
101, a distance of 3168 m. What is the
drivers speed in m/s? What is her velocity?


2.
A student walks his girlfriend to 1
st

period, a
distance of 40 m from the cafeteria. He turns
back toward the cafeteria to his class, 15 m
away. This takes 5 minutes. What is his
speed? His velocity?

Speed = 26.4 m/s

Velocity = 26.4 m/s

s = 0.18 m/s;
v=0.083 m/s

Looking Deeper at Acceleration


Constant acceleration
-

an object will change its
velocity by the
same

amount each second.


THIS IS NOT CONSTNAT VELOCITY!!!


Non
-
constant acceleration
-

an object will change
its velocity by
different

amounts each second.






Which one is constant? Non
-
constant?

Looking Deeper at Acceleration


Since accelerating objects are constantly changing
their velocity, one can say that the distance
traveled/time is not a constant value.



Time


0
-

1 s

~ 5 m/s

~ 5 m

~ 5 m



1
-
2 s

~ 15 m/s

~ 15 m

~ 20 m



2
-

3 s

~ 25 m/s

~ 25 m

~ 45 m



3
-

4 s

~ 35 m/s

~ 35 m

~ 80 m


Lets make 3 quick graphs!



Velocity

Distance
traveled in
interval

Total
distance
traveled

Looking Deeper at Acceleration


Well, you may be relieved to know that
acceleration is a vector qty with no scalar
counterpart.


So where is the direction?


The direction of the acceleration vector
depends on two things:


whether the object is speeding up or slowing down


whether the object is moving in the + or
-

direction


Looking Deeper at Acceleration


A
positive acceleration
occurs, when an
object is speeding up. Acceleration is in the
same direction as the velocity.



A
negative acceleration
occurs, when an
object is slowing down. Acceleration is in
the
opposite
direction as the velocity.

Looking Deeper at Acceleration


The general RULE OF THUMB is:




If an object is slowing down, then its

acceleration is in the opposite direction of

its motion.


*See demo*

Looking Deeper at Acceleration


Which table shows positive acceleration?
negative acceleration?







A is positive, B is negative.


Practice…



So… a car traveling at 10 m/s in a straight line
speeds up to 30 m/s in 5.0 s. What is the
average acceleration?


What are we given?


What are we looking for?


a = 4.0 m/s
2

Practice…


A shuttle bus slows down with an average
acceleration of

1.8m/s
2
. How long does it take
the bus to slow from 9.0 m/s to a complete stop?


What are we given?


What are we looking for?

Practice…


Practice makes perfect!!!

Represented as graphs


We

ll get to that later….

Graphing Motion


Three types of Graphs: D
-
T, V
-
T, A
-
T


What does slope of each represent?




This covers all the

concept

, how

s your
math skill holding up?

Position vs Time Graphs


Position goes on the vertical axis


Time is on the horizontal axis


Position vs Time Graphs


What is the position at time 4s? What about 8s?


What is the
the

avg


velocity? (think back one

slide.)



1 m/s


Position vs Time Graphs


Let

s consider this car.




The graph would look like this:


It would have a constant, rightward (+) velocity

Position vs Time Graphs


Now, let

s consider this other car.





It would have a changing rightward (+) velocity


The graph would look like this:

Position vs Time Graphs


The shapes of the position versus time graphs reveal
reveals useful information about the velocity of the
object.


It is often said, "As the slope goes, so goes the
velocity."


Whatever characteristics the velocity has, the slope
will exhibit the same (and vice versa).


Position vs Time Graphs


What can you tell me about each objects
velocity?


Object 1 has a constant

positive velocity.


Object 2 has no velocity.


Object 3 has a constant

negative velocity.

Position vs Time Graphs


Instantaneous velocity


velocity at a specific
point in time


Can be found by the tangent of a curve.

Position vs Time Graphs


What do these graphs tell you about the
velocity?






Slow, Rightward(+)Constant Velocity


Fast, Rightward(+)Constant Velocity

Position vs Time Graphs


What do these graphs tell you about the
velocity?






Slow, Leftward(
-
)Constant Velocity


Fast, Leftward(
-
)Constant Velocity

Position vs Time Graphs


What do these graphs tell you?






Negative (
-
) Velocity, Slow to Fast


Negative (
-
) Velocity, Fast to Slow


How would you make this positive?

Practice


The following graph represents the motion of a
car. What can you tell me about the car

s
motion based on the graph?





The car has a rightward velocity. The car has a
changing velocity. The car is moving from
slow to fast since the slope changes from small
big.

Practice


The following graph represents the motion of a
car. What can you tell me about the car

s
motion based on the graph?





The car has a negative velocity. The car has a
changing velocity. The car is moving from
slow to fast since the slope changes from small
to big.

Four Kinematic Equations

Four Kinematic Equations


Remember:


Constant acceleration
-

an object will change
its velocity by the
same

amount each second.


With this idea comes four kinematic equations.


Δx = ½(v
i

+ v
f
) Δt


v
f

= v
i

+ a Δt


Δx = v
i
Δt + ½ a(Δt)
2


v
f
2

=

v
i
2

+ 2 a Δx


Four Kinematic Equations


There are always 4 variables


To use these equations you guess and check.


Remember to always do 4 things:

1.
Draw a diagram

2.
Write what you know

3.
Write what you need

4.
Guess and check


Let

s practice…

Four Kinematic Equations


Ima Hurryin is approaching a stoplight moving
with a velocity of +30.0 m/s. The light turns
yellow, and Ima applies the brakes and skids to a
stop. If Ima's acceleration is
-
8.00 m/s
2
. What is
the displacement of the car during the skidding
process.


Diagram


Knowns?


Unknowns?


Equation

Four Kinematic Equations


Ben
Rushin

is
is

waiting at a stoplight. When it
finally turns green, Ben accelerated from rest at a
rate of a 6.00 m/s
2
for a time of 4.10 seconds.
Determine the displacement of Ben's car during
this time period.


Diagram


Knowns
?


Unknowns?


Equation


Four Kinematic Equations


A racing car reaches a speed of 42m/s. It then
begins a uniform negative acceleration, using its
parachute and brakes and comes to rest 3.5s later.
What is the distance that it takes the car to stop.


Diagram


Knowns
?


Unknowns?


Equation


Four Kinematic Equations


A plane starting at rest at one end of a runway
undergoes a uniform acceleration of 4.8m/s
2

for
15s before takeoff. What is its speed at takeoff?


Diagram


Knowns
?


Unknowns?


Equation



In a speed boat race the time starts when the
boat has a speed of 5m/s. It accelerates at a
constant rate of 3.3m/s
2
, with a final velocity
of 45m/s. How far was the race?

Practice makes ….


Try these



pg 53# 1
-
2, pg 55# 1
-
2, pg 58#1
-
3



Free Fall!!!!

(show video)

Free Fall!!!!

Free Fall


I
s when an object is falling under the sole
influence of gravity


Two important facts:


Free falling objects do
not

encounter air
resistance (in this class)


Free fall is a downward acceleration toward
earth (the sign gets tricky)

Free Fall


formally known as

acceleration of
gravity


= g


g = 9.81m/s
2


Often times estimated at 10m/s
2

or 9.8m/s
2


There are slight variations that are affected
by altitude, we will ignore this.

Free Fall


g is independent of 3 things:


time it

s been falling


mass of the object


if it started at rest or not

A deeper look


Think of it this way:



Δv = 9.8 m/s


Δt = 1s


This means every 1s the velocity
increases 9.8m/s


t
v
a



A deeper look


Think of it this way:



So how fast would you be going 3
seconds after jumping out an airplane?


How about 5 min?


Terminal Velocity


speed
when the
force of air resistance is equal and
opposite to the force of gravity.


(around 55m/s for humans)



t
v
a



A deeper look


Δv = 9.8 m/s


Δt = 1s


This means every 1s
the velocity increases
9.8m/s


Time (s)

Velocity

1

9.8m/s

2

19.6m/s

3

29.4m/s

4

39.2m/s

5

49.0m/s

Working Backwards


It all works backward as well.


If a ball is thrown straight up:


It will decelerate at 9.81m/s
2


At the top of it

s path the ball

hangs


in
mid air.


At bottom of it

s path the balls velocity is
equal to v
i



See Diagram….


Practice…


A worker drops a wrench from the top of a
tower 80m tall. What is the velocity when the
wrench strikes the ground?


Diagram


Knowns
?


Unknowns?


Equation


Practice…


Jason hits a volleyball so that it moves with and
initial velocity of 6m/s straight upward. If the
volleyball start 2m above the floor. How long
will it be in the air before it strikes the floor?


Diagram


Knowns
?


Unknowns?


Equation


Practice…


A ball is thrown straight up into the air at an
initial velocity of 25m/s. How long does it take
for it to reach the top of its path? How far up
does it travel?


Diagram


Knowns
?


Unknowns?


Equation


Practice makes ….


Try these



pg 64 Practice F # 1
-
4



Practice makes ….


Homework



pg 59 # 1
-
3, 5
-
6