kinematics 1.1

8/18/2019 kinematics 1.1

1/36

Raymond A. Serway

Chris Vuille

Chapter Two

Motion in One Dimension


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Kinematics defnitions

• Kinematics – ranch o! physics"study o! motion

• #osition $ x % – where you arelocated

• Distance $d % – how !ar you ha&e

tra&eled' re(ardless o! direction • Displacement $∆ x % – where you

are in relation to where you

started


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Dynamics

• The ranch o! physics in&ol&in( themotion o! an o)ect and therelationship etween that motion and

other physics concepts• Kinematics is a part o! dynamics

– *n +inematics' you are interested in thedescription o! motion

– Not concerned with the cause o! themotion

*ntroduction


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Displacement

The displacement Δx is a vector that points from the initial position to the final

position. SI Unit of Displacement: meter (m)

positioninitial=o

x positionfinal=x

ntdisplaceme=−=∆o

xxx


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Distance &s. Displacement

• ,ou dri&e the path' and your odometer(oes up y - miles $your distance%.

• ,our displacement is the shorter directed

distance !rom start to stop $(reen arrow%.• hat i! you dro&e in a circle/

start

stop


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Distance


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Speed' Velocity' 0Acceleration

• Speed $v % – how !ast you (o

• Velocity $v % – how !ast and which

way"the rate at which position

chan(es

• A&era(e speed $ v % – distance 1 time

• Acceleration $a% – how !ast you

speed

t


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stance anDisplacement

Starting from origin, O a person walks 90m east, then t!rns aro!nd and walks

"0m west#

$% &hat is the total walked distance' % *0m

$% &hat is the displacement' % +0m, d!e east


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Displacement 23amples

• 4rom A to 5 – 3i 6 78 m

– 3! 6 9: m

– ∆3 6 :: m

– The displacement is positi&e' indicatin( themotion was in the positi&e 3 direction

• 4rom C to 4 – 3i 6 7- m

– 3! 6 ;97 m

– ∆3 6 ;


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Displacement'>raphical

Section :.=


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Average Velocity

nits for velocit-% m.s, /1, km1#

t t t o

o

∆

∆=

−

−=

xxx

v

timeElapsed

ntDisplaceme velocityAverage =


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(x0, t0 )

(x2, t2 )

(x1, t1 )

(x5, t5 )

(x4, t4 )

(x3, t3 )

(x6, t6 )

point x (m) t (s)

O 0 0

A 1 1

B 5 2C 12 3

D 8 4

E 10 5

F 5 6

A

0

B

CE

D

F


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point x (m) t (s)

O 0 0

A 1 1

B 5 2

C 12 3

D 8 4

E 10 5

F 5 6


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• the specifc !eatures o! the motiono! o)ects are demonstrated y the

shape and the slope o! the lines ona position &s. time (raph.

To 2egin, consider a car moving with a constant, rightward

(+) velocity sa- of 30 m.s#


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• ?ow consider a car mo&in( witha rightward (+), changing

velocity ; that is' a car that is mo&in(ri(htward ut speedin( upor accelerating.


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Constant Velocity

Positive Velocity

Positive Velocity

Changing Velocity (acceleration)

Slow, Rightward(+)

Constant Velocity

Fast, Rightward(+)

Constant Velocity

Slow, Leftward()

Constant Velocity Fast, Leftward()Constant Velocity


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AccelerationAcceleration – how !ast you speed up'

slow down' or chan(e direction" itsthe rate at which &elocity chan(es.


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?e(ati&e Acceleration

• A ne(ati&e acceleration does notnecessarily mean the o)ect isslowin( down

• *! the acceleration and &elocity areoth ne(ati&e' the o)ect is speedin(up

• BDeceleration means a decrease inspeed' not a ne(ati&e acceleration

Section :.7

Velocity 0 Acceleration Si(n


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Velocity 0 Acceleration Si(nChart

V E L O C I T Y

AC C

E LE R A

T I ON

+

+ /oving forward4Speeding !p

/oving 2ackward4Slowing down

/oving forward4

Slowing down

/oving 2ackward4

Speeding !p

cce era on ue o


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cce era on ue o>ra&ity

9#5 m.s6

7ear the s!rface of the

8arth, all o2ectsaccelerate at the same

rate (ignoring air

resistance)#

a 6 g 6 ;


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Kinematics 4ormula Summary=or > motion with constant acceleration%


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Motion Dia(ram Summary

Section :.


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4ree 4all

• A !reely !allin( o)ect is any o)ect mo&in(!reely under the inEuence o! (ra&ity alone – 4ree !all does not depend on the o)ects

ori(inal motion• All o)ects !allin( near the earths sur!ace

!all with a constant acceleration

• The acceleration is called the acceleration

due to (ra&ity' and indicated y g

Section :.F


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Acceleration due to >ra&ity

• SymoliGed y g

• g 6


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• In 1865 Jules Verne proposed sending men to theMoon by firing a space capsule from a 220-m-longcannon with final speed of 10.97 km/s.

• What would have been the unrealistically largeacceleration experienced by the space travelers duringtheir launch?

• How much time did it took for the capsule to go fromrest to 10.97 km/s

•#28 p.51


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• A truck covers 40.0 m in 8.50 s while uniformly slowing down to a

final velocity of 2.80 m/s.• (a) Find the truck’s original speed.

• (b) Find its acceleration.

• #29 p.51


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• A Cessna aircraft has a liftoffspeed of 120 km/h.

• (a) What minimum constantacceleration does the aircraftrequire if it is to be airborne after

a takeoff run of 240 m?• (b) How long does it take theaircraft to become airborne?

• #31 p.52


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• In a test run, a certain caraccelerates uniformly from zero to

24.0 m/s in 2.95 s.• (a) What is the magnitude of thecar’s acceleration?

• (b) How long does it take the car tochange its speed from 10.0 m/s to20.0 m/s?

• #33 p.52


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• A train is traveling down a straighttrack at 20 m/s when the engineer

applies the brakes, resulting in anacceleration of -1.0 m/s2 as longas the train is in motion.

• How far does the train moveduring a 40-s time intervalstarting at the instant the brakesare applied?

• #37 p.52


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• A ball is thrown vertically upward with a speed of 25.0 m/s.

• (a) How high does it rise?• (b) How long does it take to reachits highest point?

• (c) How long does the ball take tohit the ground after it reaches itshighest point?

•(d) What is its velocity when itreturns to the level from which itstarted?

• #45 p.52


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• A baseball is hit so that it travelsstraight upward after being struck

by the bat. A fan observes that ittakes 3.00 s for the ball to reachits maximum height.

• Find (a) the ball’s initial velocityand

• (b) the height it reaches.

• #54 p.53

kinematics 1.1

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