First evidence of study of mechanics traced back to Ancient Sumeria. First systematic studies conducted by the Ancient Greeks around 300 B.C.

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1 Serway AP Physics Ch 2 1 dimensional motion-kinematics dynamics-study of motion that involves force and mass. Kinetics-study of motion without regard to causes. First evidence of study of mechanics traced back to Ancient Sumeria. First systematic studies conducted by the Ancient Greeks around 300 B.C. At the same time Aristotle ( B.C. As well as Claudius Ptolemy 140 A.D.) put forth the groundwork for the Geocentric model.-earth Centered Universe. This is mentioned because it wasn't until the 17 th century where people started to question this position. Nicolaus Copernicus ( ), Johannes Kepler, and Galileo Galilei ( ) develop the heliocentric model where the earth orbits the sun and the modern mechanics revolution is born. 2.1 Displacement Motion of an object from one place in space and time to another 2.2 Velocity From Aristotle: Speed distance traveled in a given amount of time so many miles in so many hours Average speed = distance traveled/time elapsed slight difference from above *Speed is independent of the direction of motion has only a scale or size. It is a scalar quantity. Speed is a scalar, does not tell us where it is going. The average velocity is the vector formed by the ratio of the displacement, measured from the starting point of the motion. Constant speed uniform speed corresponds to equal distance in equal intervals of time of any fixed duration, however small. Or simply it is the total distance traveled by total time elapsed ex 2.1

2 Velocity is a vector quantiy having magnitude and direction v x t units are m/s and can be positive or negative v=52m-30m/10s-0s=2.2 m/s see below picture above illustrates the difference in average speed vs average velocity. Both have same average velocity but blue line travels a greater distance so has greater average speed. Graphs above show position v. time. Chart on the left illustrates a car moving at constant velocity, the second picture is a graph of table 2.1. The graphs are different because the car has a velocity that changes. A line drawn through any point shows the velocity of the car at that point. Generally there is a different velocity between any 2 points. Instantaneous velocity Since x gets smaller as t shrinks, we can locate slope at P (our instantaneous speed). the derivative v = x/ t. Speed is the derivative of x with respect to t. As average velocity gets infinitely small, time gets infinitely small Would not make sense to have a distance at a real time 0, nothing moves there. By shrinking time interval to approaching 0 to get instantaneous velocity. The magnitude of the instantaneous velocity vector equals the instantaneous speed V speed is the magnitude of velocity. The velocity vector at any point is tangent to the path pointing in the direction of the motion. Basically, it is a point tangent to the curve of a x vs t graph. Ex 2.2

3 2.3 Acceleration In 300 B.C. Philosopher physicist Strato hinted at acceleration equal increments of distance are traveled in shorter and shorter times. In the 12 th century a new idea of velocity acceleration occurs when, during equal periods of time, a body travels greater and greater distances. But it wasn t until the 14 th century where velocity must be included. Accleration is the time- rate of change of velocity. A= v/ t You can have acceleration when there is a change in direction a horse is moving at a constant action on a merry go round or change in magnitude of force - horse getting faster and faster or when both situations occur. If the rate of change in velocity/time is opposite of the positive direction deceleration occurs. Instantaneous Acceleration a=lim as t approaches v t exp 2.3 plus quick quiz active figures 2.12 a-c

4 Uniform acceleration happens when equal changes in speed occur during equal intervals of time, of any duration. The steeper the line, the greater the acceleration. The slope tangent to the motion graph of velocity vs line represents instantaneous acceleration. Uniformly Accelerated Motion In reality, acceleration is almost never constant, but since not using calculus, have to accept uniform acceleration. If the equation looks at acceleration as a Scalar, in straight line motion, we have an interval (t) since we start t, at O. Example A Jag from km/h (60mph) to O of acceleration in 3.7s. Compute scalar value km/h 26.83m/s The Mean Speed 1375 to relate a to distance traveled. So they wondered if there was an average value of the speed for an object that is uniformly accelerating along a straight line. Happens to be the mean speed. For a body accelerating uniformly, the mean speed Vav is the height of the mid point of the straight line speed time graph. And the area under the curve is the distance traveled. 2.5 one dimensional motion Integrate Intervals By having many of these rectangles they become smoother, to where they become a bunch of instantaneous velocities therefore, the area under the curve is the distance traveled. v=v 0 + at Equations for Constant Acceleration Average speed = Vav ½ (Vi + Vf) Mean speed = X = Vav = ½ (Vi + Vf)t Now plug in Value for Vf Distance traveled with constant acceleration.

5 Ex 2.4, 2.5, 2.6, 2.7

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7 Free Fall Acceleration is most nearly constant. But air resistance affects the speed of an object in a vacuum all objects fall at the same rate regardless of weight. Aristotle saw that following bodies descend at different rates proportional to their individual weights. Which is ok for very light objects such as feathers in air. But accorrding to this idea, a stone 10x heavier then a feather the stone fell 10x faster. When an object falls in air, it reaches a point where they can go no faster because of air pushes up Terminal speed Generally, terminal speed decreases with a decrease in size. A BB at 9m/s is slower than a cannon ball 250m/s even though both are round. Light objects with a large surface have a very low terminal speeds. Acceleration of Gravity Strato, Aristotle s successor correctly states that objects in free fall accelerate. Like a stream of water droplets. They start as a stream, but break up into droplets. This could not happen if the droplets were not accelerating such that the drops farther away pull away from the slower ones. Acceleration is constant for all bodies, but depending on your place on Earth,their rate will vary. All equations for uniform motion can be used substituting g for a. g is always acting downward. Ex ,2.10