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Calculus In Physics By: May Cheung

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**One-Dimensional Motion**

Examples: a car moving on a straight road a person walking down a hallway a sprinter running on a straight race course dropping a pencil throwing a ball straight up a glider moving on an air track and many others...

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Derivatives The position graph s(t), where x is time and the y is distance The velocity graph v(t), is the derivative of the position graph, based on how quickly the distance is changing The acceleration graph a(t), is the derivative of the velocity graph, based on how quickly the velocity is changing

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**Position This graph records the distance that is travel**

Let’s use the example of a person that is walking the distance either increases or decreases relative to where the starting point is but to make things easier right (forward) is positive and left (backward) is negative

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Velocity this graph based on the slope of the position graph meaning how slow or how fast the person is traveling A positive slope – the person is walking to the right and the distance is increasing An increase in the positive slope - the person is walking faster so the distance is increasing at a faster rate A decrease in the positive slope – the person is walking slower so the distance is increasing at a slower rate Zero slope – the person has walking and no distance has been traveled

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Cont. Zero slope – the person has stopped and no distance has been traveled A negative slope - the person is walking in the negative direction (left) so the distance is decreasing An increase in the negative slope – the person is walking faster in the left direction so the distance is decreasing at a faster rate An decrease in the negative slope – the person is walking slower in the left direction so the distance is decreasing at a slower rate

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Acceleration This graph is based on the slope of the velocity meaning how fast or how slow the person is changing his pace For example : walking to walking faster as opposed to walking to running a positive slope – the person changes from walking to running, increasing the pace of its travel at a exponential pattern (3 ft/sec to 9 ft/sec to 81 ft/sec) Zero slope – the person changes from walking to walking faster at a consistent pattern (2 ft/sec to 4 ft/sec to 6 ft/sec) a negative slope – the person changes from running to walking, decreasing the pace of its travel at an exponential pattern (81 ft/sec to 9 ft/sec to 3 ft/sec)

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Acceleration Acceleration – the rate at which velocity changes Can be an: Increase in speed Decrease in speed Change in direction.

Acceleration Acceleration – the rate at which velocity changes Can be an: Increase in speed Decrease in speed Change in direction.

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