Kinematics equations for motion with constant acceleration (1) (2) (3) (4) 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

Derivation of Kinematic Equations of motion at Constant Acceleration

Testing Kinetics for a=9.80m/s2 Free Fall

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 Newton's Principal Contributions The laws of motion The law of gravity The nature of light Calculus (Method of Fluxions) Mathematical approximation methods (1642 – 1727)

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” 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). Wear seat belts!

Newton’s Second Law of Motion If 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 FGP = - FPG Force exerted on the Ground by the Person Force exerted on the Person by the Ground

pulling a sled, Michelangelo’s assistant 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 For forward motion: FAG> FAS FSA > FSG

Derivation of the Lorentz transformation The simplest linear trans formation Principle of relativity Consider expanding light Substitute 1/c from the lower to the upper equation Divide each equation by c

Solve for Find transformation for the time t’ We had