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# Deriving displacement as a function of time, acceleration, and initial velocity

AP.PHYS:
CHA‑4.A (EU)
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CHA‑4.A.1 (EK)
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CHA‑4.A.1.1 (LO)
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CHA‑4.A.2 (EK)
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CHA‑4.A.2.1 (LO)
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CHA‑4.A.2.3 (LO)
Displacement in physics is a vector quantity that measures the change in position of an object over a given time period. Learn how to calculate an object’s displacement as a function of time, constant acceleration and initial velocity. Created by Sal Khan.

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• Does the mass of the Earth ever change? •   Yes it does, actually. But very slowly. Consider debris and other particulate matter reaching earth from space. This will increase the mass of earth, all be it very minimally. Also, consider launching satillites and shuttles into orbit. These are materials from earth that have mass that have left the planet. These are very small changes, but over time (say millions of years) the mass of earth has increased.
• So far what I have studied is that g is positive downwards and negative upwards... you are confusing me by saying that it is negative downwards... please clear this concept! • What is the difference between little 'g' and big "G"? •  G is the "Gravitational constant" - however, it is not just a number. It does have the dimension [N (m/kg)²]. You can easily see, why it has to be that way by looking at the law of universal gravitation and checking the units ... It's value is approximately 6.67E-11 and it has been found empirically (see Cavendish experiment).

On the other hand, g is usually used to denote the (average) acceleration an object near the earths surface experiences due to the gravitational attraction of the earth. It has an approximate value of 9.81 m/s² which means that, ignoring the effects of air resistance, the speed of an object falling freely near the Earth's surface will increase by about 9.81 meters per second every second.

Note: as an acceleration, g is a vector quantity. It's direction is towards the center of the earth.
• What does force mentioned in the video exactly mean? •  In physics, a force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. It is measured in the SI unit of newtons and represented by the symbol F. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or a flexible object to deform, or both. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
• when Sal tells at that up is positive and down is negative should it be he other way round,because the work done is against gravity so up will be negative and the 'g' will be positive since its in the same direction? • That is a good question. In physics and engineering for example, it doesn't actually matter which direction you select for positive and negative. They are conventions you can set yourself and become "stated assumptions". As long as you are consistant in your direction conventions, it is entirely acceptable to select either direction to be positive. I hope that helps.
• Sorry that this is such a base question but at why did Sal divide the a times delta t term by 2? • If there were no air resistance on Earth, would there be a terminal velocity? • well,(I am aware this is 7 years ago, but incase someone needs it, here you go) I'd say, it depends because an object would not travel at terminal velocity at AIR as there is no air resistance to balance out the weight of the object, so it would accelerate due to gravity. As for an object falling through WATER, or some fluid.. It would travel at terminal velocity as the weight of the object equals upthrust(Assuming Viscous drag negligible) so the answer is yes, there would be terminal velocity, but not for objects falling through air, Basically the medium at which it falls would be whats important in this case.
Hope this helps someone!
• i have a question which i think is related to this topic:
Two balls of masses m1 and m2 are thrown vertically upward with the same speed u. If air resistance is neglected, they will pass through their point of projection in the downward direction with a speed x. find x.   