DISPLACEMENT AND VELOCITY Chapter 2-1. Objectives Describe motion in terms of frame of reference,...
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Transcript of DISPLACEMENT AND VELOCITY Chapter 2-1. Objectives Describe motion in terms of frame of reference,...
Objectives
Describe motion in terms of frame of reference, displacement, time and velocity.
Calculate displacement, velocity and time interval.
Interpret position vs. time graphs.
Kinematics deals with the concepts that are needed to describe motion.
Dynamics deals with the effect that forces have on motion.
Together, kinematics and dynamics form the branch of physics known as Mechanics.
2.1 Displacement
As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called displacement.
Displacement is the change in position of an object.
Displacement doesn’t always tell you distance an object moved.Displacement = final position – initial position∆x = xf-xo
Si units – meters (m)
2.1 Displacement
Displacement is not always equal to the distance traveled.Displacement can be positive or negative.
If displacement is positive, the object moves to the right.
If the displacement is negative, the object moves to the left.
2.2 Speed and Velocity
Average speed is the distance traveled divided by the timerequired to cover the distance.
timeElapsed
Distance speed Average
SI units for speed: meters per second (m/s)
2.2 Speed and Velocity
Average velocity is the displacement divided by the elapsedtime.
timeElapsed
ntDisplaceme velocityAverage
ttt o
o
xxx
v
SI units for velocity: meters per second (m/s)
2.2 Speed and Velocity
Velocity gives both direction and magnitude (amount) while speed only gives the magnitude - no directionAverage velocity does not tell you the speed or velocity
of the moving object at each moment or instant.
Average velocity can be positive or negative depending on direction moved.
Time can never be negative!
Average Velocity:
0 2 4 6 8 10 12 140
1
2
3
4
5
6
7
Position vs. Time
t (s)
x (m
)
The slope of a position vs. time graph is called the average velocity.
‘Should get something similar to this from your lab data’
o
oAV tt
xx
t
xv
Average Velocity
0 1 2 3 4 5 60
1
2
3
4
5
6
7
8
t (s)
x (m
)
The definition of average velocity holds even if the slope changes.
This would be the slope of the line connected the final and initial points.
if
ifAV tt
xx
t
xv
Average Velocity:
0 2 4 6 8 10 12 140
2
4
6
8
10
12
14
Position vs. Time
t (s)
x (m
)
Steeper slope means a faster moving object.
Speed and velocity:
Velocity and speed can be used interchangeably in everyday languageIn Physics, however, there is a distinction:
Speed is a Scalar quantity (numerical value = magnitude only)
Velocity is Vector quantity - Describes motion with both direction and a numerical value (magnitude and direction)
Constant Velocity Model: Velocity vs. Time Graph
0 1 2 3 4 50
1
2
3
4
5
6
position (m)Linear (posi-tion (m))
t (s)
v (m
/s)
With constant velocity,
On a graph of velocity vs. time, displacement can be calculated by finding the area under the graph.
If the velocity is negative, the displacement calculate will be negative.
tvx AV
mtvx AV 1535
Constant Velocity Model: Velocity vs. Time Example
0 1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
4
5
t (s)
v (
m/s
)
Use the graph to calculate the displacement of the object:From 0 s to 3 sFrom 3 s to 6 sFrom 6 s to 9 sFrom 0 s to 9 s
More practice:- ‘GUESS’ method
A vehicle travels 2345 m in 315 s toward the evening sun. What is its velocity?Given: Displacement = 2345 m , time = 315 sUnknown: Velocity = ?Equation and model: (kinematics)Separate the unknown: -----Substitute and solve: V = 2345 / 315
7.44 m/sdoes the answer make sense?
• Yes!!
(REVIEW)Displacement for constant acceleration
The displacement from time 0 to time t is the area under the velocity graph from 0 to t.
Area = ½ b h
t (s)
v (m/s)
))((21 vtx
)10)(5(21x
mx 25
Instantaneous Velocity – write this under
your instantaneous acceleration paragraph
The instantaneous velocity indicates how fastthe car moves and the direction of motion at eachinstant of time.
tt
xv
0lim
2.3 Acceleration
• The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs.
• Acceleration is the measure of how fast something speeds up or slows down
2.3 Acceleration
ss
m
ttt o
o
.
vvva
DEFINITION OF AVERAGE ACCELERATION
SI units for acceleration: (m/s2)
2.3 AccelerationExample 3: Acceleration and Increasing Velocity
Determine the average acceleration of the plane.
G: U: E: (kinematics)
S:S:
sm0ov
hkm260v s 0ot s 29t
249.2 sma
a
o
o
tt
vv
a
s 0s 29
sm02.72
sm
tt o
ovva
2.3 AccelerationExample 3: Acceleration and decreasing Velocity
Calculate the average accelerationG: U: E: (kinematics)
S:
S:
sm28ov
sm13v
s 9ot s 12t
a
o
o
tt
vv
a
s 9s 12
sm2813
sm
tt o
ovva
2sm0.5a
Graph for speeding up motion – Acceleration describe the following motion
Position vs. Time
00.5
11.5
22.5
33.5
44.5
0 0.5 1 1.5 2 2.5 3
time (s)
posit
ion (
m)
Everyday examples of such motion include: Driving a car Throwing a ball Kids sliding at the playground
Changes in velocity:
Instantaneous acceleration:Since in some situations, the acceleration of an
object can be constant , as a result, it will be the same value at any instant of time.
The plus or minus sign before the number indicates the two possible directions for the acceleration vector when the motion is along a straight line.
Interpret The Graph Below:Distance vs. Time ( constant negative velocity)
This object is ________________
Interpret The Graph Below:Distance vs. Time (acceleration)
The curve in the graph shows that _______________
Interpret The Graph Below:Distance vs. Time (deceleration)
The curve in the graph shows that the objects _______________
Interpret The Graph Below:Distance vs. Time
In the first part of the graph the object is ____________
In the second part of the graph the object is _______________
In the third part the object is ___________
Interpret The Graph Below:Velocity vs. Time (constant acceleration)
The objects velocity is ______________ this is known as ____________
The straight line shows that the object is moving at a _____________
Interpret The Graph Below:Velocity vs. Time
The objects velocity is _________________
The straight line shows that _______________
2.4 Equations of Kinematics for Constant Acceleration
Equations of Kinematics for Constant Acceleration
tvvx o 21
221 attvxx oo
atvv o
axvv o 222
2.4 Equations of Kinematics for Constant Acceleration
G: U: E: (kinematics)
S:
S: m 110
?x2
21 attvx o
2221 s 0.8sm0.2s 0.8sm0.6
2.4 Equations of Kinematics for Constant Acceleration
Example 6 Catapulting a Jet
Find its displacement.
2.4 Equations of Kinematics for Constant Acceleration
G:
U: E: (kinematics)
S:
S: m 62x
sm0ov2sm31a
sm62v
??x
a
vvx o
2
22
2
22
sm312
sm0sm62 x
Free Fall acceleration:
An object thrown or dropped in the presence of Earth’s gravity experiences a constant acceleration directed toward the center of the earth.
This acceleration is called the free- fall acceleration, or the acceleration due to gravity.Free fall acceleration is the same for all objects,
regardless of their mass.
Free fall acceleration:
The value for free fall acceleration used in this book is: g = 9.81 m/s2.
In this book, the direction of the free fall acceleration is considered to be negative because the object accelerates toward earth.
Negative
Positive
Free fall acceleration:Since gravity on earth is constant at
9.81m/s2,If 2 objects of different masses are dropped
from the same height, they will both hit the ground at the same time considering no air resistance. No matter what their masses are.
If there is air resistance, some objects may be slowed down
The more surface area an object has, the more air resistance it will experience.ex. A wadded piece of paper will fall faster than a flat
piece of paper which will experience more air resistance due to its larger surface area
Free fall acceleration:
Describe the acceleration of the object as it falls off the cliff – notice the change in velocity after each second of fall
Free fall acceleration:
All objects, when thrown up will continue to move upward for some time, stop momentarily at the peak, and then change direction and begin to fall.
Velocity at the top of the arc is 0 m/s
What goes up must come down!!In an upward displacement of an
object, as soon as the ball is released with an initial positive velocity, it has an acceleration of -9.81m/s2, causing the object to slow down until it stops momentarily. It then changes direction moving downward with an increasing velocity.
Distance vs. Time and Velocity vs. time graph of an object thrown up in the presence of gravity
2.6 Freely Falling Bodies
Example 10 A Falling Stone
A stone is dropped from the top of a tall building. After 3.00sof free fall, what is the displacement, y, of the stone?
Example 10: A falling stone2.6 Freely Falling Bodies
G: , U: E: (kinematics)
S:
S: m 1.44y
221 attvy o
2221 s 00.3sm80.9s 00.3sm0 y
2.6 Freely Falling Bodies
Example 12 How High Does it Go?
The referee tosses the coin upwith an initial speed of 5.00m/s.In the absence of air resistance,how high does the coin go aboveits point of release?
Example 12: How high does it go?2.6 Freely Falling Bodies
G: , vU: E:
(kinematics)
S:
S:
ayvv o 222 a
vvy o
2
22
m 28.1y
2
22
sm80.92
sm00.5sm0
y
2.6 Freely Falling Bodies
Conceptual Example 15 Taking Advantage of Symmetry
Does the pellet in part b strike the ground beneath the cliffwith a smaller, greater, or the same speed as the pelletin part a?