Intro to Motion – Ch. 2

2.1 FRAME OF REFERENCE (COORDINATE SYSTEM)

The context in which we study motion

Includes a reference point and a directional system

1-D vs. 2-D vs. 3-D

TWO TYPES OF QUANTITIES

1 Vector Quantities Indicate both magnitude and directionHow much? Which way?

All vector quantities must be defined in relation to

some reference point… The Origin

Vector quantities (in one dimension) can be + or -, depending on their position relative to the reference point

Ex.… velocity, acceleration, force, displacement

2 SCALAR QUANTITIES

• Scalar quantities only indicate magnitude• How much?

• Distance traveled is a scalar quantity• It only tells you the length

of the path, not which way you went

• Examples• Mass, temp, volume,

density, speed, energy

WHERE IS THE OBJECT? Position (x)

The separation between the object and some reference point.An object’s locationxi – initial positionxf - final position

Distance Traveled (d)The total distance required to get from one position to

another

Displacement (x )The change in position relative to a reference point

x = xf – xi How are they different?

DISPLACEMENT VS. DISTANCE TRAVELED

Flight 93 Example

2.2 – SPEED & VELOCITY•Average Speed

• v = distance/t

• scalar equivalent of velocity • “magnitude of velocity”• Doesn’t depend on direction• Often times equivalent in magnitude as velocity

• Units m/s

VELOCITY

HOW FAST IS THE OBJECT TRAVELING?

• Average Velocity (vavg)• equal to the total displacement

divided by the time interval during which the displacement occurred

• Units are usually m/s or any unit of length over a unit of time

t

xvavg

VELOCITY IS A VECTOR QUANTITY

• It has magnitude AND direction

• Must define a frame of reference

• Can be positive or negative, depending on the DIRECTION of movement, not the location of object

INSTANTANEOUS VELOCITY• Velocity at one specific instant

• An average is taken over some time interval (∆t), whereas instantaneous occurs at one specific time

• If we make the time interval (∆t) smaller and smaller it will eventually represent an a very good approximation of

instantaneous velocity

AVG SPEED & AVG VELOCITY - NOT THE SAME

• Speed• speed is the rate of motion• speed is always positive and gives no information about

direction of motion• greater the speed of an object, the faster it moves.

• Velocity• gives both rate of motion and its direction• sign of velocity gives direction of motion• magnitude of the velocity is the speed of motion

2.3 POSITION-TIME GRAPHS

SLOPE

PG. 57

2.4 EQUATION OF MOTION• Position described as a function of time

• xf=xi+vt same as v=Δx/t• Notice the agreement with y=mx+b

format as it pertains to P-t graphs

AIR RESISTANCE As an object is falling air resistance is

acting on it and slowing it down faster the object moves through air goes

the stronger the air resistance is Also influenced by surface area

There is a point where a falling object is going so fast the air resistance becomes so strong that the object can no longer accelerate….. This velocity is called terminal velocity

Object is still falling, but no longer accelerating

In most problems we ignore any affects of air resistance

SKYDIVE / FREE FALL RECORD

• Kittinger- 1960• Video

• Failed attempts• Failed Skydive Attempt• Skydiver

• RedBull Stratos Project• Launch date TBD

• Red Bull Stratus Project• http://www.space.com/7824-skydiver-plans-supersonic-jump-edge-sp

ace.html

• http://spacejump.co.uk/history.htm • http://www.popularmechanics.com/technology/aviation/safety/space-

dive-the-race-to-jump-from-120000-feet

• Other project details• Videos

RELATIVE MOTION…

How was this video shot??

KNIGHT RIDER ….. ??

MOTION IS RELATIVE… Before we can quantify motion with

velocity, we have to know how it is defined

All motion is relative to something else

Usually measure motion relative to

Earth, but important to understand that there is no universal reference frame

◦ Cars on a highway◦ Knight Rider

Moving observers view motion differently… think of as a moving frame of reference