DISPLACEMENT AND VELOCITY Chapter 2-1. Objectives Describe motion in terms of frame of reference, displacement, time and velocity. Calculate displacement,

DISPLACEMENT AND VELOCITY

Chapter 2-1

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.

Describing Motion: this slide is not in your notes!

Are these two motions different?

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.

position initial ox

position final x

ntdisplaceme oxxx

2.1 Displacement

m 0.2ox

m 0.7x

m 0.5x

m 0.5m 2.0m 7.0 oxxx

2.1 Displacement

2.1 Displacement

m 0.2x

m 0.7ox

m 0.5x

m 0.5m 7.0m 2.0 oxxx

m 0.2ox

m 0.7x

m 0.5x

m 0.7m .02m 5.0 oxxx

2.1 Displacement

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!!

CLASS ASSIGNMENT / HOMEWORK

I will not accept late work

Acceleration

Section 3

(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 Acceleration

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

2.3 Acceleration

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

The graph shows __________

Interpret The Graph Below:Distance vs. Time (constant velocity):

The object is __________

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 velocity)

The objects is _______

Interpret The Graph Below::Velocity vs. Time

The objects 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 _______________

Interpret The Graph Below:Velocity vs. Time

The objects velocity is _________________

Interpret The Graph Below:Velocity vs. Time

The objects velocity is _________________

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

CLASS ASSIGNMENT / HOMEWORK

I will not accept late work

Chapter 2

Section 6:

Falling Objects

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

2.6 Freely Falling Bodies

2sm80.9g

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

An apple and a feather falling at the same rate absent air resistance (vacuum)

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?

2.7 Graphical Analysis of Velocity and Acceleration

sm4s 2

m 8 Slope

t

x

2.7 Graphical Analysis of Velocity and Acceleration

2.7 Graphical Analysis of Velocity and Acceleration

2.7 Graphical Analysis of Velocity and Acceleration

2sm6s 2

sm 12 Slope

t

v

CLASS ASSIGNMENT / HOMEWORK

I will not accept late work