PHY 231 1 PHYSICS 231 Lecture 2: Motion in 1 dimension, part I Remco Zegers.

PHY 2311

PHYSICS 231Lecture 2: Motion in 1 dimension,

part I

Remco Zegers

PHY 2312

Galileo (1564-1642)

What mathematical forcesgovern accelerated motion?

A wooden and stone sphere are dropped from the tower of pisa. Which one reaches the earth first?

Answer: same time!

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The inclined plane experiment

Distance traveled goes with the square of time:x(t)~t2

Time measured with water!

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Displacement

X=0 X=30 X=45

t=0 t=1X=30

X=0 X=30 X=45

t=0t=1X=-30

Displacement is a vector and thus has direction (sign)Displacement is not equal to Distance

PHY 2315

Average Velocity

Average velocity=Displacement

Time interval

if

if

tt

xx

t

xv

X=0 X=30 X=45

t=0 t=1 t=2

t=0 t=1 t=2

Which object has the largest average velocity over 2 s?

Same!

PHY 2316

Graphically x(m)

t(s)

The average velocity is the slope of the line connecting begin end end point in the x-t graph. Ignore what happens in between.

if

if

tt

xx

t

xv

= slope

PHY 2317

Vectors and Scalars...

X=0 X=30 X=45

t=0t=1X=-30

if

if

tt

xx

t

xv

Average velocity:vector=-30

if

if

tt

xx

t

xspeed

=+30Average speed:scalar

PHY 2318

Instantaneous Velocity

“But officer, my average speed was only 25 miles per hour...”

Sometimes we want to know the speed at one particularpoint in time.

PHY 2319

PHY 23110

Instantaneous velocity x(m)

t(s)

if

if

tt

xx

t

xv

What is the Velocity at t=2.0 s?

Consider the average velocity for a very small time intervalwith t=2.0 s in the center!

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Instantaneous velocity

x(m)

t(s)

t

xv

t

0lim

t

x

PHY 23112

Instantaneous velocity

x(m)

t(s)

t

xv

t

0lim

t

x

v=slope of the tangent to the x-t curve at t=2.0 sThink about the sign!

tangent

t

xv

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Question

t

x

Which object had the largest average velocity?Which object had the largest instantaneous velocity?

A B

B

if

if

tt

xx

t

xv

tangent

t

xv

B

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Acceleration

t

x

A change in slope in thex-t graph…

t

v…means a change in velocity:Acceleration

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Acceleration

if

if

tt

vv

Average acceleration

t

va

t

0lim

tangent

t

va

Instantaneous acceleration:

PHY 23116

Question

t

v t=0,v=20

t=1, v=5

What is the average acceleration between t=0 and t=1

A) 15 B) -15 C) 0 D) infinity

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Constant positive velocity

PHY 23118

Positive velocity and acceleration

PHY 23119

Question

Which v-t diagram matches which a-t diagram?

GALILEO!