kinematics 1.1.pdf

7/24/2019 kinematics 1.1.pdf

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Raymond A. Serway

Chris Vuille

Chapter Two

Motion in One Dimension


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Kinematics definitions

Kinematicsbranch of physics; study of

motion

Position (x)where you are located

Distance (d)how far you have traveled,

regardless of direction

Displacement (x)where you are inrelation to where you started


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Dynamics

The branch of physics involving the motion ofan object and the relationship between thatmotion and other physics concepts

Kinematicsis a part of dynamics In kinematics, you are interested in the description

of motion

Notconcerned with the cause of the motion

Introduction


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Displacement

positioninitialox

positionfinalx

ntdisplacemeo

xxx

The displacementxis a vectorthat points from the initial position to the final

position. SI Unit of Displacement:meter (m)


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Distance vs. Displacement

You drive the path, and your odometer goes up by 8miles (your distance).

Your displacement is the shorter directed distance

from start to stop (green arrow). What if you drove in a circle?

start

stop


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Distance


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Speed, Velocity, & Acceleration

Speed (v)how fast you go

Velocity (v)how fast and which way;

the rate at which position changes Average speed ( v)distance/time

Acceleration (

a

)how fast you speedup, slow down, or change direction;the rate at which velocity changes


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Distance and Displacement

Starting from origin, O a person walks 90-m east, then turns around and walks

40-m west.

Q: What is the total walked distance? A: 130-m

Q: What is the displacement? A: 50-m, due east


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Displacement Examples

From A to B xi= 30 m

xf= 52 m

x = 22 m

The displacement is positive, indicating the motionwas in the positive x direction

From C to F xi= 38 m xf= -53 m

x = -91 m

The displacement is negative,

indicating the motion was in

the negative x direction Section 2.1

i l


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Displacement,

Graphical

Section 2.1


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Average Velocity

ttto

o

xxx

v

Units for velocity: m/s, MPH, kmPH.

timeElapsed

ntDisplacemevelocityAverage


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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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i t ( ) t ( )


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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 specific features of the motion of

objects are demonstrated by the shape and

the slope of the lines on a position vs. timegraph.

To begin, consider a car moving with a constant, rightward

(+) velocity- say of +10 m/s.


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Now consider a car moving with a rightward (+),

changing velocity- that is, a car that is moving

rightward but speeding up or 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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AccelerationAccelerationhow fast you speed up, slow

down, or change direction; its the rate atwhich velocity changes.


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Negative Acceleration

A negative acceleration does not necessarily

mean the object is slowing down

If the acceleration and velocity are both

negative, the object is speeding up

Deceleration means a decrease in speed,

not a negative acceleration

Section 2.3


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Velocity & Acceleration Sign Chart

V E L O C I T Y

A

C

C

EL

E

R

A

T

I

O

N

+ -

+ Moving forward;Speeding up

Moving backward;

Slowing down

- Moving forward;Slowing down

Moving backward;

Speeding up


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Acceleration due to Gravity

9.8 m/s2

Near the surface of the

Earth, all objectsaccelerate at the same

rate (ignoring air

resistance).

a= g= -9.8 m/s2

Interpretation: Velocity decreases by 9.8 m/s each second,

meaning velocity is becoming less positive or more

negative. Less positive means slowing down while going

up. More negative means speeding up while going down.

This acceleration

vector is the

same on the way

up, at the top,

and on the way

down!


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Kinematics Formula SummaryFor 1-D motion with constantacceleration:


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Motion Diagram Summary

Section 2.4


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Free Fall

A freely falling object is any object moving freely

under the influence of gravity alone

Free fall does not depend on the objects original motion

All objects falling near the earths surface fall with aconstant acceleration

The acceleration is called the acceleration due to

gravity, and indicated by g

Section 2.6


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Acceleration due to Gravity

Symbolized by g

g= 9.80 m/s

When estimating, use g 10 m/s2

gis always directed downward Toward the center of the earth

Ignoring air resistance and assuming gdoesnt varywith altitude over short vertical distances, free fall is

constantly accelerated motion

Section 2.6


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Combination Motions

Section 2.6


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In 1865 Jules Verne proposed sending men to theMoon by firing a space capsule from a 220-m-long

cannon with final speed of 10.97 km/s.

What would have been the unrealistically large

acceleration experienced by the space travelers duringtheir launch?

How much time did it took for the capsule to go from

rest to 10.97 km/s

#28 p.51 =

2 =

2

=10,970/ 0

2(220) = 273502 /

= 10,970 /

= 0 /

= 220

=

=

=

=10,970/

273,502/= 0.04


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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 trucks original speed.

(b) Find its acceleration.

#29 p.51


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A Cessna aircraft has a liftoff

speed of 120 km/h.

(a) What minimum constantacceleration does the aircraft

require if it is to be airborne after

a takeoff run of 240 m? (b) How long does it take the

aircraft to become airborne?

#31 p.52


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In a test run, a certain car

accelerates uniformly from zero to

24.0 m/s in 2.95 s. (a) What is the magnitude of the

cars acceleration?

(b) How long does it take the car tochange its speed from 10.0 m/s to

20.0 m/s?

#33 p.52


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A train is traveling down a straight

track at 20 m/s when the engineer

applies the brakes, resulting in anacceleration of -1.0 m/s2as long

as the train is in motion.

How far does the train moveduring a 40-s time interval

starting at the instant the brakes

are applied?

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A ball is thrown vertically upwardwith 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 it

returns to the level from which itstarted?

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A baseball is hit so that it travels

straight upward after being struck

by the bat. A fan observes that ittakes 3.00 s for the ball to reach

its maximum height.

Find (a) the balls initial velocityand

(b) the height it reaches.

#54 p.53

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