Kinematics Distance (meters) Displacement (meters + direction) Δx = xf – xi

Instantaneous vs avg. speed/velocity Speed (m/s) Velocity (m/s + direction) – rate of displacement

change Acceleration (m/s2) – rate of change of velocity

The 3 Kinematic equations

There are 3 major kinematic equations than can be used to describe the motion in DETAIL. All are used when the acceleration is CONSTANT.

)(2

21

2

1

22

2

oo

oo

fi

o

xxavv

attvxx

tvvx

atvv

Kinematics for the VERTICAL DirectionAll 3 kinematics can be used to analyze one

dimensional motion in either the X direction OR the y direction.

)(2)(2

21

21

2222

22

ooyyoox

oyooxo

oyyo

yygvvxxavv

gttvyyattvxx

gtvvatvv

Summary

t (s) t (s) t (s)

x (m)v (m/s) a (m/s/s)

slope

= v

slope

= a

area = Δxarea = Δv

During which time interval is velocity largest?

During which time interval is velocity zero?

During which time interval is velocity negative?

During which time interval is the object slowing down?

During which time interval is the object moving in the negative direction?

Horizontally Launched ProjectilesProjectiles which have NO upward trajectory and NO initial

VERTICAL velocity.

0 /oyv m s

constantox xv v

Horizontally Launched ProjectilesTo analyze a projectile in 2 dimensions we need 2

equations. One for the “x” direction and one for the “y” direction. And for this we use kinematic #2.

212oxx v t at

oxx v t

Remember, the velocity is CONSTANT horizontally, so that means the acceleration is ZERO!

212y gt

Remember that since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is equal to ZERO.

Vertically Launched ProjectilesYou will still use kinematic #2, but YOU MUST use

COMPONENTS in the equation.

vo

vox

voy

q

oxx v t 212oyy v t gt

cos

sinox o

oy o

v v

v v

Example

A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.

(a) How long is the ball in the air?

(b) How far away does it land?

(c) How high does it travel?

v o=20

.0 m

/s

= 53q

cos

20cos53 12.04 /

sin

20sin53 15.97 /

ox o

ox

oy o

oy

v v

v m s

v v

v m s

ExampleA place kicker kicks a

football with a velocity of 20.0 m/s and at an angle of 53 degrees.

(a) How long is the ball in the air?

What I know What I want to know

vox=12.04 m/s t = ?voy=15.97 m/s x = ?

y = 0 ymax=?

g = - 9.8 m/s/s

2 2

2

1 0 (15.97) 4.92

15.97 4.9 15.97 4.9

oyy v t gt t t

t t t

t

3.26 s

Example

A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.

(b) How far away does it land?

What I know What I want to know

vox=12.04 m/s t = 3.26 svoy=15.97 m/s x = ?

y = 0 ymax=?

g = - 9.8 m/s/s

(12.04)(3.26)oxx v t 39.24 m

Example

A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.

(c) How high does it travel?

CUT YOUR TIME IN HALF!

What I know What I want to know

vox=12.04 m/s t = 3.26 svoy=15.97 m/s x = 39.24 m

y = 0 ymax=?

g = - 9.8 m/s/s

2

2

12

(15.97)(1.63) 4.9(1.63)

oyy v t gt

y

y

13.01 m

Newton’s First Law – The Law of Inertia

INERTIA – a quantity of matter, also called MASS. Italian for “LAZY”. Unit for MASS = kilogram.

Weight or Force due to Gravity is how your MASS is effected by gravity.

mgW NOTE: MASS and WEIGHT are NOT the same thing. MASS never changesWhen an object moves to a different planet.

What is the weight of an 85.3-kg person on earth? On Mars=3.2 m/s/s)?

Newton’s First LawAn object in motion remains in motion in a

straight line and at a constant speed OR an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) Force.

00 Facc

Free Body Diagrams

A pictorial representation of forces complete with labels.

W1,Fg1 or m1g

•Weight(mg) – Always drawn from the center, straight down•Force Normal(FN) – A surface force always drawn perpendicular to a surface.•Tension(T or FT) – force in ropes and always drawn AWAY from object.•Friction(Ff)- Always drawn opposing the motion.

m2g

T

T

FN

Ff

Newton’s Second Law

The acceleration of an object is directly proportional to the NET FORCE and inversely proportional to the mass.

maFm

Fa NET

NET

FFNET

Tips:•Draw an FBD•Resolve vectors into components•Write equations of motion by adding and subtracting vectors to find the NET FORCE. Always write larger force – smaller force.•Solve for any unknowns

N.S.L

A 10-kg box is being pulled across the table to the right by a rope with an applied force of 50N. Calculate the acceleration of the box if a 12 N frictional force acts upon it.

mg

FNFa

Ff

2/8.3

101250

sma

a

maFF

maF

fa

Net

Inclines

cosmg

sinmg

mg q

FNFf

q

qq

q

q

Tips•Rotate Axis•Break weight into components•Write equations of motion or equilibrium•Solve

Newton’s Third Law“For every action there is an EQUAL and

OPPOSITE reaction. This law focuses on action/reaction pairs (forces) They NEVER cancel out

All you do is SWITCH the wording!• PERSON on WALL• WALL on PERSON

Work Done by a Force Work can be found by W = F*d*cosϴ

Work is also equal to the change in energy Measured in joules

Power