Chapter 3

Linear Motion

5. DESCRIPTION OF MOTION

• Speed

• Velocity

• Acceleration

Speed

Average Speed = distance/timeUnits - m/s, ft/s, etc.

Instantaneous Speed is the speed you would read from a

speedometer

Distance vs. Time graph

Time

Dis

tanc

e

Instantaneous Speed is the slope of this graph at a point

Average Velocity

Time

Dis

tanc

e

Find end-points Connect with a line Find slope of the line

Choose Different End-Points

Time

Dis

tanc

e

Find end-points Connect with a line Find slope of the line

Example of Average Speed

• You take a trip from A to B and back to A.

• You want to average 60 mph for the round trip A to B to A.

A B2 miles

• From A to B you average 30 mph.• What is your average speed on the

return trip from B to A?

30 mph

Velocity

• Average Velocity = Displacement/time

Units - m/s, ft/s, etc.

• Instantaneous Velocity of an object is

its instantaneous speed plus the

direction it is traveling

• Velocity is a vector.

Displacement and Average Velocity

D

t

Dv

Distance traveled is the length of the path taken.

ntDisplacemeD

Average velocity =

Acceleration

• Acceleration = "change" in velocity/time

Units - m/s2, ft/s2, etc.

• Acceleration is also a vector

Vel

ocity

Time

Acceleration is the slope of a Velocity vs. Time graph.

t

va

Motion at constant velocity

Accelerated motion

Here Here, too

• Demo - Ball on incline and ball on table

• Deceleration = negative acceleration

Acceleration on Galileo's Inclined Planes

(equal time slices)

Velocity and Acceleration

• Galileo used inclined planes to study accelerations.

• He found constant accelerations for inclines. (It was too hard to measure time for free-falls.)

• He also found that the mass of the objects didn't matter.

Relationships Between v and a for Linear Motion

t

vva 0

atvv 0

atvv 0

atv If initial velocity is zero, then

or

t

va

Example

A jogger starts at zero velocity with an acceleration of 3 ft/s2. How fast is she moving after 4 seconds?

00 v atv 2/3 sfta

st 4

)4(/3 2 ssftv

sftv /12

6. FREE FALLMotion near the surface of the earth in the absence of air resistance.

The acceleration of an object is

g = 32 ft/s2 = 9.8 m/s2

How Fast

Velocity in gravitational field (starting from rest)

v = gt = 32t English

Or v = 10t Metric

atvv 0

Distance Equation

221 gttvdd oo

do = initial distance

vo = initial velocity

g = acceleration due to gravity

Free Fall

Falling in a gravitational field:Take do and vo to be zero

(object starts from the origin at rest)

Then: d = do + vot + ½at2 becomes

d = ½gt2

d = 5t2 (Metric)

Free FallTime of Fall

(s)Velocity Acquired

(m/s) – 10tDistance Fallen

(m) – 5t2

1

2

3

4

5

10

20

30

50

40

125

80

45

20

5

Demonstrations• Demo - Reaction timer• Demo - Paper and book drop

Free Fall Graphs

0

5

10

15

20

25

0 0.5 1 1.5 2

Time (s)D

ispl

acem

ent (

m)

0

5

10

15

20

25

0 0.5 1 1.5 2

Time (s)

Vel

ocity

(m

/s)

0

2

4

6

8

10

12

0 0.5 1 1.5 2

Time (s)

Acc

eler

atio

n (m

/s/s

)

Ball released from rest, down positive, measure distance from point of release.

Different Assumptions

0123456

0 0.5 1 1.5 2

Time (s)D

ispla

cem

ent (m

)

-15

-10

-5

0

5

10

15

0 0.5 1 1.5 2

Time (s)

Vel

ocity

(m

/s)

-12-10

-8-6-4-20

0 0.5 1 1.5 2

Time (s)

Acc

eler

atio

n (m

/s/s

)

Ball thrown up from origin with an initial speed of 10 m/s, up is positive

Free Fall - How QuicklyHow Fast

• Acceleration Is How Quickly - How Fast -Changes in Velocity

• Acceleration is difficult to understand because it is a rate of a rate.