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Free Fall Acceleration If you tossed an object either up or down and could somehow eliminate the effects of air on its flight, you would find that the object accelerates downward at a certain constant rate. That rate is called the free-fall acceleration, and its magnitude is represented by g. The acceleration is independent of the object’s characteristics, […]

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Another Look at Constant Acceleration The first two equations in Table 2- I are the basic equations from which the others are derived. Those two can be obtained by integration of the acceleration with the condition that a is constant. To find Eq. 2- I I, we rewrite the definition of acceleration (Eq. 2-8) as We next write […]

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PROBLEM·SOLVING TACTICS TACTICS : SOLVING TACTICS.Check the Dimensions The dimension of a velocity is L/T -that is, length L divided by lime T-and the dimension of an acceleration is L/T2, In any equation, the dimensions of all terms must be the same, If you are in doubt about an equation, check its dimensions. To check the dimensions of […]

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Constant Acceleration:Special Case In many types of motion. the acceleration is either constant or approximately so. For example. you might accelerate a car at an approximately constant rate when a traffic light turns from red to green. Then graphs of your position. velocity, and acceleration would resemble those in  (Note that a (T) in  is constant, which requires that […]

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Sample Problem A particle’s position on the x axis  is given by with x in meters and t in seconds (a) Find the particle’s velocity function vet) and acceleration function aft). SOLUTION:One key idea is that to get the velocity function v(t) , we difference the position the position function x (t) with respect to time.here […]

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PROBLEM SOLVING TACTICS Tactic 5: An Acceleration’s Sign In common language, the sign of an acceleration has a nonscientific meaning: positive acceleration means that the speed of an object is increasing, and negative acceleration means that the speed is decreasing (the object is decelerating). In this book, however, the sign of an acceleration indicates a direction, […]

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Acceleration When a particle’s velocity changes, the particle is said to undergo acceleration (or to accelerate). For motion along an axis, the average acceleration over a time interval  is where the particle has velocity 1′, at time t, and then velocity 1’2 at time t2.The instantaneous acceleration (or simply acceleration) is the derivative of the velocity with respect to […]

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Sample Problem The position of a particle moving on an x axis is given by   with x in meters and ( in seconds. What is its velocity at ( = 3.5 s? Is the velocity constant, or is it continuously changing? SOLUTION :Fo r simplicity, the units have been omitted from Eq. 2-5, but you can […]

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Sample Problem Is an x«() plot for an elevator that is initially stationary, then moves upward (which we take to be the positive direction of .r), and then stops. Plot v as a function of time. SOLUTION: The Key idea here is that we can find the velocity at any time from the slope of the curve of […]

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Instantaneous Velocity and Speed You have now seen two. ways to describe how fast something moves: average velocity and average speed. both of which are measured over a time interval . However, the phrase “how fast” more commonly refers to how fast a particle is moving at a given instant-and that is its instantaneous velocity (or simply velocity) […]