Kinematics

Types of QuantitiesAlmost all quantities have units

- examples: meters, seconds, kilograms- Without units numbers would be meaningless

Vector – Quantities that includes both magnitude and a direction Vectors can be drawn They are represented by arrows

Example: 12 m south

Scalar – Quantities that do not include direction (magnitude only)Example: 4 seconds

http://www.youtube.com/watch?v=A05n32Bl0aY

Distance vs Displacement

• Distance is a scalar quantity: direction doesn’t matter

• Displacement is a vector– Direction matters– Straight line route from where you started to

where you end (as the crow flies)– MUST HAVE A DIRECTION

What is the Distance traveled?

8 m

6 m

2 m

1 m

d = 8 m + 6 m + 2 m + 1 md = 17 m

-

What is the displacement?

8 m

6 m

2 m

1 m

How can we interpret distance-time graphs?

Do Now:

Mark off a distance of 5 m on the floor and time how long it takes a ball to roll the distance. Repeat this three different times with three different speeds.

Ball # Distance (m) Time (s)

1

2

3

Speed (m/s)

Now graph distance vs. time for each ball

Distance (m)

Time (s)

Calculate the speed of each ball

Slope

Find the slope of the three lines

x

yslope

12

12

xx

yy

= =if

if

tt

dd

=t

d

df =final distance

di = initial distance

tf = final time

ti = initial time

Do you notice anything special about the slope of a line on a distance-time graph?

It is equal to the speed or velocity

t

dv

v = average velocity

The physical significance of the slope of a distance-time graph is average velocity!!!

Distance (m)

Time (s)

Describe the motion that this graph is representing

Slope is constant

Since slope = speed, speed is constant

Slope is positive

Therefore speed is positive (forward)

The red car is moving with a greater velocity and therefore has a greater slope

Distance (m)

Time (s)

Describe

Slope is zero, therefore velocity is zero

In other words, the object is at rest

Calculate the velocity

Distance (m)

Time (s)

300

0 30

t

dv

ss

mm

030

3000

= -10 m/s

Distance (m)

Time (s)

Describe the motion that this graph is representing

Slope is constant

Since slope = speed, speed is constant

Slope is negative

Therefore speed is negative (backward)

1 2 3 4 5 6

50

40

30

20

10

Time (s)

Distance (m)

Calculate v for:

A

B C

D

:AB

:BC

:CD

smss

mm

t

dv /50

01

050

smss

mm

t

dv /0

13

5050

smss

mm

t

dv /25

35

500

Describe the motion:

Const. vel. forward

At rest

Const. vel. backward

What is the:

Total distance

Total displacement

100 m

0 m

:AB

:BC

:CD

2

1

0

-1

-2

Distance (m)

Time

1. Where is the velocity zero?

2. Where is the velocity constant?

3. Where is the ball moving forward?

4. Where is the ball moving backward?

5. What is the total distance traveled?

6. What is the resultant displacement?

A

B C

D E

AB

AB

BC

CD

CD

,

DE,

6 m

-2 m