Kinematics equations for motion with constant acceleration

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200 2

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Position ( ):A quantity which describes the location of the object in one, two, or three dimensions. Velocity ( ):A quantity which describes the change of position with respect to time

Acceleration ( ):A quantity which describes the change of velocity with respect to time

(1)

(2)

(3)

(4)

v

x

a

Derivation of Kinematic Equations of motion at Constant Acceleration

Testing Kinetics for a=9.80m/s2

Free Fall

2

2

1aty

atv

All objects fall with the same constant acceleration!!

• In air…– A stone falls faster than a

feather

• Air resistance affects stone less

• In a vacuum– A stone and a feather will

fall at the same speed.

Newton’s Laws of Motion

(1642 – 1727)

Newton's Principal Contributions

• The laws of motion

• The law of gravity

• The nature of light

• Calculus (Method of Fluxions)

• Mathematical approximation methods

Newton’s First Law of Motion

An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity as long as no force acts on it

Newton’s First Law of Motion“Law of Inertia”

Wear seat belts!

Inertia: the tendency of an object to resist changes in its state.

The First Law states that all objects have inertia. The more mass an object has, the more inertia it has (and the harder it is to change its state).

Newton’s Second Law of MotionIf we want to change the state of an object, we should apply force on it.“The net force on an object is equal to the product of its mass and acceleration, or F=ma.”

Contact Force = acts on an object only by touching it.

Long-Range Force = forces that are exerted without contact or forces resulting from action-at-a-distance

Short-Range Force

Newton’s Third Law of Motion: Action- Reaction

For every action there is an equal and opposite reaction.

pulling a sled, Michelangelo’s assistant

Force exerted on the Ground by the Person

Force exerted on the Person by the Ground

FGP = - FPG

pulling a sled, Michelangelo’s assistant

For forward motion: FAG> FAS FSA > FSG

Michelangelo’s assistant has been assigned the task of moving a block of marble using a sled. He says to his boss, "When I exert a forward force on the sled, the sled exerts an equal and opposite force backward. So, how can I ever start it moving? No matter how hard I pull, the backward reaction force always equals my forward force, so the net force must be zero

Derivation of the Lorentz transformation

The simplest linear trans formation

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)'('

)('

vyxx

vtxx

Principle of relativity

Consider expanding light

)''(

)('

vtctct

vtctct

Divide each

equation by c

)1('

)1('

c

vtt

c

vtt

Substitute 1/c from the lower to the upper equation

)1('' 2

c

vtt

Solve for 2

2

22

22

1

1

1

1

cv

cv

Find transformation for the time t’

We had

c

xt

c

vtt

vtxx

vtxx

)1('

'

)('

)''('

cvcvx

t

c

vxtt

2

2

2

1

)('