Kinematics The study of how objects move. Where are You? We must start with a question.

KinematicsThe study of how objects The study of how objects

movemove

Where are You?

We must start with a

question

PositionReference Point:

Zero location in a coordinate system or frame.

Frame of Reference:

Coordinate system used to define motion.

Position: Separation between an object and a reference point. It needs a distance and direction.

i.e. 3.0 meters to the right.

To find where you are you need the following:

You are Here

You are Here

You are Here

You are Here

You are Here

You are Here

You are Here

You are Here

Distance vs. Displacement

Distance is simply the total path length traversed in moving from one location to another

Distance is a SCALAR quantity. A measurement with only magnitude, or size.

50 m

Distance vs. Displacement

Displacement is the straight-line distance between two points, along with the direction from the starting point to the final position.

Displacement is a VECTOR quantity. A measurement with magnitude, or size and a direction

10 m East

Difference between Distance and Displacement

Walking to

Physics Lab

Distance = 8 mDisplacement = 8m right

Right - PositiveLeft - Negative

Direction Convention :Displacement =+8m

Speed

SpeedTime

Distance

Speed is the rate at which distance is traveled.

=10 m/s

20 m

2 sec

Speed m

202sec

Speed is a scalar

quanity

Average speedAverage speed is the distance d traveled, the actual path, divided by the total time t elapsed in traveling that distance.

Average Speed Distance TraveledTotal Time

Instantaneous SpeedInstantaneous Speed is how fast an object is moving at a

particular instant of time.

Average vs. Instantaneous Speed

Velocity

V xt

x xt t

o

o

xo

to

VelocityVelocity tells how fast something is moving and in what direction. Velocity is a vector quantity.Average VelocityAverage Velocity is the

displacement divided by the total travel time =initial position,

commonly zero

= initial time, commonly zero

V xt

When xo and to are zero

A jogger jogs from one end to the other of a straight 300 meter track (from point A to point B) in 2.50 min and then turns around and jogs 100 m back toward the starting point (to point C) in another 1.00 min. What are the jogger’s average speeds and velocities in going

A) From A to BB) From A to C after turning around

Speed and

Velocity Problem

avg speed dt

ms

ms

300150

2 00.

v xt

ms

B

B

ms

300150

2 00.

A)

v x xt t

m ms sc

B C

B C

ms

300 100150 60 0

0 952( ).

.

Given:xB = 300m - 0m = +300m (from A to B)xC = 200m – 300m = -100m (from B to C)tB = 2.50 min = 150 stC = 1.00 min = 60.0 s

B)

Average speed and velocity from A to B

Average speed and velocity from A to Cavg speed

dt

m ms s

ms

300 100150 60 0

190.

.

Two Compone

nts of Velocity

GraphicGraphical look al look

at at MotionMotion

AcceleratioAccelerationnPosition is the separation between

an object and a reference point. Displacement is a change in positionVelocity is the time rate change of displacementAcceleration is the time rate change of velocityAll four are vector quantitiesRepresented by a magnitude and direction

Kinematic Equations

v dt

d dt t

2 1

2 1

d dt

2 1

a vt

v vt t

2 1

2 1

v vt

2 1

v v at2 1

accelerationacceleration

velocityvelocity

v dt

v v v

1 2

2

dt

v v1 2

2With a constant acceleration

Total Displacement and total time

Average Velocityd v v t 1

2 1 2( )

d v v t 12 1 2( ) v v at2 1 v at1

d v v at t 12 1 1( ( ))

d v t at 12 1

12

22( )

d v t at 11

22

d v v t 12 1 2( )

v v ad22

12 2

d v va

2

212

2d v v v va

1 2 2 1

2

t v va

2 1

d vt

v v at2 1 v v1 2

2v v v

1 2

2 v va

2 1

Kinematic Equations

v dt

v v at2 1

a vt

d v t at 11

22

v v ad22

12 2

Problem:

Ally the Alligator takes off from an airfield. She starts from rest and obtains a velocity of 36 m/s at take off in 20.0 seconds.

What is her acceleration down the runway?

How far did she go down the runway?a vt

v vt

2 136 0

20

ms

ms

sec18 2. m

s

18 2. ms

d v v t 12 1 2( )d m

sms 1

2 0 36 20 0( ) . secd m360