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Linear Motion Unit 1

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Motion occurs all around us. Motion is easy to recognize, but it is hard to describe. Even the Greek scientists of more than 2000 years ago had great difficulty describing motion. They failed because they didn’t understand the idea of rate. A quantity divided by time is a rate. It tells how fast something happens, or how much something changes in a certain amount of time. For our understanding, we’ll consider only motion in a straight line- linear motion.

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Motion is relative to something else. For example, when we say that a racing car reaches a speed of 300 km/h, we mean relative to the track.

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Speed A measure of how fast something is moving The rate at which distance is covered Defined as the distance covered per unit of time Instantaneous speed- the speed at any instant Average speed- total distance covered divided by the time interval it takes

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Velocity Speed in a given direction To have a constant velocity we must have both constant speed & constant direction. Motion at a constant velocity is motion in a straight line at constant speed. If either the speed or the direction is changing, then the velocity is changing.

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Acceleration Change of velocity divided by the time interval We can change the state of motion by changing its speed, its direction of motion, or both. These are changes in velocity. The rate at which the velocity is changing is called acceleration.

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Do objects accelerate while falling? We know objects start from a rest position & gain speed as they fall. Gravity causes the object to accelerate downward once it begins falling. Such objects are in free fall & only affected by gravity. Freely falling objects accelerate at 10 m/s for each second of elapsed time. That means after 1 second, the object is moving at 10 m/s; after 2 seconds, 20 m/s; after 3 seconds, 30 m/s…

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Consider an object thrown straight up. It continues to move upward for awhile, then it comes back down. At the highest point, when the object is changing direction of motion from upward to downward, its instantaneous speed is 0. It then starts downward just as if it has been dropped from rest. During the upward part of this motion, the object slows from its initial upward velocity to 0. Its speed decreases at 10 m/s, the same rate that it increases when moving downward.

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How fast something moves is entirely different from how far it moves- speed and distance are not the same thing. For an easy mathematical way to figure out the distance of falling objects, we use the formula: d=1/2gt 2

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Formulas Average speed (v)= distance traveled elapsed time Average velocity (v)= displacement elapsed time Acceleration (a)= change in velocity elapsed time

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Benjamin watches a thunderstorm from his window. He sees the flash of a lightning bolt and begins counting the seconds until he hears the clap of thunder 10 seconds later. Assume the speed of sound in air is 340 m/s. How far away was the lightning bolt?

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Free fall formulas Displacement of a falling object: d= v o t + 1/2gt 2 Final velocity of a falling object: v f 2 = v o 2 + 2gd v f = v o + gt

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King Kong carries Fay Wray up the 321m tall Empire State building. At the top, Fay Wray’s shoe falls from her foot. How fast will the shoe be moving when it hits the ground?

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