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Kinematics- Acceleration Chapter 5 (pg. 81-103) A Mathematical Model of Motion

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The Nature of Acceleration Acceleration is the rate of change in _______ with time - the rate at which the velocity changes. If an object is speeding up, it is __________ ! If an object is slowing down, it is ! If an object has constant speed, but is changing direction, it is ! -this is the case when an object travels in a circular path at constant speed ANY VELOCITY CHANGE is an ACCELERATION ! velocity accelerating

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a = v - v o ∆t This is the basic definition of acceleration in the form of an equation. The following equations are basic equations which are derivations of our basic definitions of velocity and acceleration for objects moving with constant acceleration: m/s 2 are the units of acceleration ( think meters per second CHANGE in velocity per second of time)

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A car accelerates from rest at a rate of 2.00 m/s 2 west for 8.50 s. What is the velocity of the car at this time? What was its displacement during this time? v i = 0m/s a = 2.00 m/s 2 west ∆t = 8.50 s v = ? ∆ d = ? v = 0 + (2.00 m/s 2 west )(8.50 s) v = 17.0 m/s west ∆ d = 0 + 0(8.5) + 0.5(2.00 m/s 2 west)(8.50s) 2 d = 72.3 m west

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3) An object is accelerated to 35.0 m/s at a rate of 2.00 m/s 2 for a time of 7.34 s. How far did it move during this time? Hint: find initial velocity first, it’s not 0 m/s. 1) How far does an object travel if it accelerates from 12.0 m/s to 45.0 m/s in 15.3 s? 2) An object traveling 48.7 m/s is brought to a stop in 7.61 s. How far did the object move during this time? 4) An object rolled up a hill will stop after having traveled up the hill 18.0 m. If the object is slowed at a rate of 2.50 m/s 2, what was the initial velocity and how long will it take to stop rolling? Work out each problem just like the example problem provided on the previous slide. Provide the sketch, given, basic equation, working equation and answer with units. [436m] [185m] [203m] [3.80s]

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Basic Equations:

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Acceleration Acceleration is the rate of change of velocity.

Acceleration Acceleration is the rate of change of velocity.

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