1stle lecture 04 - r2 average and instantaneous acceleration(a)

8/11/2019 1stLE Lecture 04 - R2 Average and Instantaneous Acceleration(a)

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Objectives

1

Analyse 1D motion using verbal, graphicaland algebraic representations

Describe motion in 1D in terms of average

and instantaneous accelerations


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Velocity/Speed: corresponds to a change

in position

Acceleration: change in velocity

2

speed direction


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Lecture 4: Average & instantaneous acceleration

Accelerate in the direction of velocityspeed upAccelerate in the direction of velocityspeed up

Accelerate against velocityslow down

Accelerate in the direction of velocityspeed up

Accelerate against velocityslow downAccelerate at an angle to velocitychange direction


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4

Successive pictures were taken at equal intervals of

time, in which of the following exhibits acceleration?


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5

NO

NO

YES

YES

Speeding up!

Slowing down!

Successive pictures were taken at equal intervals of

time, in which of the following exhibits acceleration?


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Acceleration is the rate of

change of velocity with time.Acceleration,

Commonly expressed in

m/s2

Acceleration is how the

speed and directionof

the objects motion are

changing

Velocity is how fast and

in what directionan

object moves.

=

6


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Graphical analysis of velocity as

a function of time

Velocity,

Time,

graph

velocity at time velocity at time

7


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Graphical analysis of average

and instantaneous acceleration

Average acceleration,

=

=

Slope of the line

connecting (,) and(,)

8


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Instantaneous

acceleration, Limit of the average

acceleration as thetime interval

approaches zero

= lim

=

=

=

2

2

Slope of the

line tangent

to a point inthe plot

9


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10




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Sign conventions for both

velocity and acceleration

Samesigns (+ + or - -): object is speeding up

Differentsigns (+ - or - +): object is slowing down

> 0, > 0 moving to the right, speeding up

< 0, < 0 moving to the left, speeding up

> 0, < 0 moving to the right, slowing down

< 0, > 0 moving to the left, slowing down11


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Sample problem:

a) The object is slowing down at a decreasing rate.

b) The object is slowing down at an increasing rate.

c) The object is speeding up at a decreasing rate.d) The object is speeding up at an increasing rate.

e) The objects speed is changing at a steady rate.

12

Graphical analysis.

Which of the followingdescriptions of the motion

depicted on the graph

is most accurate?


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Sample problem:Graphical analysis.

Which of the followingdescriptions of the motion

depicted on the graph

is most accurate?a) The object is slowing down at a decreasing rate.

b) The object is slowing down at an increasing rate.

c) The object is speeding up at a decreasing rate.d) The object is speeding up at an increasing rate.

e) The objects speed is changing at a steady rate.

13

*decreasing slope


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Sample problem:

Velocity and acceleration from a plot.

A

B

D

14

C

E

THINGS TO LOOK FOR:

1.CURVATURE - acceleration

2.SLOPE - velocity


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Sample problem:


15

THINGS TO LOOK FOR:

1.CURVATURE-UPWARD> 0-DOWNWARD < 0-NONE (ZERO)

= 0

2. SLOPE (recall)-POSITIVE > 0-NEGATIVE< 0

-NONE (ZERO) = 0

NOTE: The greater the curvature,

the greater the acceleration

in the + ordirection

The greater the slope, thegreater the velocity.


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Sample problem:


A

B

D

16

C

E


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Sample problem:


A

B

D

17

C

E

Curvature:

UPWARD

Curvature:

UPWARD


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Sample problem:


A

B

D

18

C

E

Curvature:

UPWARD

Curvature:

UPWARD

Curvature:

DOWNWARD


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Sample problem:


A

B

D

19

C

E

Curvature:

UPWARD

Curvature:

UPWARD

Curvature:

ZERO

Curvature:

ZERO

Curvature:

DOWNWARD


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Sample problem:


20

Pt Curve ax

A Up +B 0 0

C Down -

D 0 0E Up +


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Sample problem:


A

B

D

21

C

E


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Sample problem:


A

B

C

D E

22


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Sample problem:


24

Pt Slope vx

A + +B + +

C 0 0

D - -E - -

S l bl


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Sample problem:


25

Pt Curve ax Slope vx

A Up + + +

B 0 0 + +C Down - 0 0

D 0 0 - -

E Up + - -


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Again:

slope of x-t graph:average velocityslope of tangent line of x-t graph:instantaneous

velocity (sometimes instantaneous is dropped)

curvature of x-t graph: acceleration

slope of v-t graph:average acceleration

slope of tangent line of v-t graph: instantaneous

acceleration (sometimes instantaneous is dropped)

26


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slope of constant = 0What s lope would yield to a


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28

In each acceleration interval, the acceleration equations apply.

When axis constant:

vx-t is a straight line

x-t is a parabola

When ax= 0:

vx-t is constant

x-t is a straight line

axis

constant

axis

constant

axis

constant

ax= 0 ax= 0 ax= 0

slope of constant = 0

slope of straight line = constant

slope of parabola = straight line

What s lopewould yield to a

cons tant or zero?

a isa is


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29

axis

constant

axis

constant

axis

constant

ax= 0 ax= 0 ax= 0

axis constant: vx-t is a straight line ax= 0: vx-t is constant

vx-t constant

vxt constant

a isa is


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30

axis

constant

axis

constant

axis

constant

ax= 0 ax= 0 ax= 0

axis constant: vx-t is a straight line ax= 0: vx-t is constant

a isa is


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31

axis

constant

axis

constant

axis

constant

ax= 0 ax= 0 ax= 0

ax= 0: x-t is a straight lineaxis constant: x-t is a parabola

parabolaparabola

parabola

straight

line

straight

line

straight line

(t>40)

(v0)

a isa is


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32

axis

constant

axis

constant

axis

constant

ax= 0 ax= 0 ax= 0

ax= 0: x-t is a straight lineaxis constant: x-t is a parabola


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33

What is the instantaneous accelerationat t = 10s?

Answer: v-t slope at 5 to 15s constant (no change in velocity)

acceleration from 5s to 15s; a(10s) = 0

Notice: +slope of x-t plot = + velocity and -slope of xt plot = - velocity


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Seatwork- solve problems in your

notebooks

- write the answers only inyour bluebook

- indicate the date

August 14, 20141. Blah?

2. Blah blah!

3. Blah blah blah!

4. Blah blah blah blah!

34


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Seatwork

35

Find the average x-acceleration,

and describe whether the speed

increases or decreases for each

of these time intervals:1-2) t1=1.0s to t2=3.0

3-4) t1=5.0s to t2=7.0s

5-6) t1

=9.0s to t2

=11.0s

7-8) t1=13.0s to t2=15.0s

t(s) vx (m/s)1.0 0.8

3 1.2

5 1.67 1.2

9 -0.4

11 -1.013 -1.6

15 -0.8=

=

Hint: Graphing maybe helpful in checking your answer

S t k 9 10


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Seatwork 9, 10.


Sketch the and plots from the given plot.

36


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TWTh: Lecture (LP104)

F: Recitation QuizTWHFAde Vera (LP104)TWHFA-1Zosa (F201)

TWHFA-2Nayga (F202)

TWHFA-3De Los Reyes (F206)TWHFA-4Olaya (F207)

TWHFA-5Bendicio (F210)

Topic: Lectures 1 and 2 (Chapter 1)

Physical quantities, units, dimensional

analysis, scalars and vectors

1.Attendance will be checked once the recit teacher enters the room:


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Case 1: if the number of present students is ODD (if all are present OR 2, 4, are

late/absent)

- have a raffle (using index card) among the present students; 1 lucky raffle winner

can choose which group he/she want to answer the recit for the day, therefore, we

will have 1 group with 3 members; while other groups will have a pairCase 2: if the number of present students is EVEN (if 1, 3, are late/absent)

- no raffle, students can pair among themselves

2. Late students (as penalty) will have to answer the recit quiz on his/her own.

Those who come to class AFTER the end of the attendance roll-call will be

considered late. If the student comes before the end of the attendance roll-call,he/she will be accepted and considered NOT LATE even if his/her name was

already called.

3. Recitation quizzes shall be done in closed notes, students may discuss with

their partner and encouraged to consult the recit teacher. Students are only

allowed to use real calculators (not the ones from their tablets, laptops orcellphones)

4. Recit solutions will be submitted by group/pair. Write the complete solution to

each problem and box the final answer.

5. If a student complains about the partner, the recit teacher can arrange rotation

t f th t it i

1stle lecture 04 - r2 average and instantaneous acceleration(a)

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