Motion and

VelocityDisplacement in Time and Space

Ft. Per Second

MPH

Meters/Sec.

Work = Force x Distance

Machines Produce Work by Transforming Energy or Changing the Direction or Distance Through Which a

Force Acts

Machines, Mechanisms and Motion are Intimately Related

Motion or Movement is a Change In Position Called Displacement

10 ft.

Position A

Position B

Speed is the Rate of Displacement

10 ft.

Position A Position B

10

0

Seconds

sec/1sec10

10DistanceSpeed ft

ft

Time

Velocity is the Rate of Displacement in a Specified Direction

10 ft.Position A Position B

10

0

Seconds

sec/1sec10

10DistanceSpeed ft

ft

Time

EastSouth

WestNorth

Speed Equations

An object’s speed is a function of Displacement (change in position) and Time (change in time

between positions)

)(

)(

12

12

ttt

dddSpeed

Speed Equations

A simple and useful version of the Speed Equation Looks Like This

Time

DistanceSpeed

If You Want to Know the Distance Traveled

Time

DistanceSpeed

TimeSpeed Distance

You Can Rewrite the Equation Like This

Position-Time Graphs

Dis

tanc

e in

Fee

t

Time in Seconds0 1 2 3 4 5 6 7 8 9

40

120

160

200

80

Describes the Rate of Change in Position of an Object Over Time

Distance (ft) Vs. Time (sec.)DistanceTime

6080

100120140160

180

20

2345678

9

1

40

Position-Time Graph

Dis

tanc

e in

Fee

t

Time in Seconds0 1 2 3 4 5 6 7 8 9

40

120

160

200

80

The Slope is Equivalent to the Average Speed

Distance (ft) Vs. Time (sec.)

Run

RiseSlope

Time

DistanceSpeed

Rise

Run

Position-Time Graph

Dis

tanc

e in

Fee

t

Time in Seconds0 1 2 3 4 5 6 7 8 9

40

120

160

200

80

How Fast is this Object Moving?

Distance (ft) Vs. Time (sec.)

20sec.Δt

Speed = 20ft/sec.

Rise 80 ft.

Run 4 sec.

80ftΔd

Time

DistanceSpeed

4sec.

80ftSpeed

Position-Time Graph

Dis

tanc

e in

Fee

t

Time in Seconds0 1 2 3 4 5 6 7 8 9

40

120

160

200

80

Distance (ft) Vs. Time (sec.)

The Slope of this Line Remains Constant Throughout the Graph

The constant slope indicates that the speed of the object remains constant

Position-Time Graph

Dis

tanc

e in

Fee

t

Time in Seconds0 1 2 3 4 5 6 7 8 9

40

120

160

200

80

The Speed of This Object

Changes Over Time

Distance (ft) Vs. Time (sec.)

B

C

A

Speed @C = 50 ft/secSpeed @A = 5 ft/sec Speed @B = 24 ft/sec

The Object is Accelerating

VelocitySlope

Average Speed Time GraphsSp

eed

in f

t/se

cond

Time in Seconds0 1 2 3 4 5 6 7 8 9

10

30

40

50

20

Describes the speed of an object at specific times and the total displacement but NOT the Direction

Study this graph and answer the questions that follow

Spee

d in

ft/

seco

nd

Time in Seconds0 1 2 3 4 5 6 7 8 9

10

30

40

50

20

How fast was this thing moving, 5 Seconds after it began to move?

Hint: It began moving after 1 second

Average Speed Time Graphs

Spee

d in

ft/

seco

nd

Time in Seconds0 1 2 3 4 5 6 7 8 9

10

30

40

50

20

Answer: 40 ft/second

Average Speed Time Graphs

Spee

d in

ft/

seco

nd

Time in Seconds0 1 2 3 4 5 6 7 8 9

10

30

40

50

20

What was the total Displacement of this thing?How far did the thing go during the whole trip?

Average Speed Time Graphs

Spee

d in

ft/

seco

nd

Time in Seconds0 1 2 3 4 5 6 7 8 9

10

30

40

50

20

Answer: This Thing Traveled a total of 175 FeetDistance = Speed x Time. Therefore the total distance is the sum of the areas of each of the

5 rectangles! Try it….It works.

Average Speed Time Graphs

Another Difference Between Speed and Velocity

Scalar Quantities (One Number)

One Gallon

Distance

Speed (MPH)

Voltage

Vector Quantities (More Than One Number)

Machine Screw Specification (tpi,length,diameter,head style)

Pant Sizes (Waist and Length)

Velocity (Speed and Direction)

Velocity is a Vector Quantity

Speed is a Scalar Quantity

Vectors Graphically Describe DIRECTION and MAGNITUDE

One Foot/sec

One Foot/sec

One Foot/sec

++ =

3 Feet/sec

And You can Add and subtract Them!

The Length of a Vector is Proportional to It’s Magnitude

6 Centimeters

6 MPH

A Vector Describing a Velocity of 6 MPH is Drawn With a Length of 6 Units

6 Inches

Scaling Vectors

Point B Point C

Point A

Vectors Can Describe Displacement

Total Displacement12.2 miles North East of the

Starting Position

10 miles East

7 miles North

The Black Dashed Line is called th

e Resultant

The magnitude of the Resultant Vector is found using the Pythagorean Theorem.

B2

C2

A2

A2 + B2 = C2

The End

Now…….Get Moving!