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CHS Physics Instantaneous Velocity &Acceleration

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Recall that this is the velocity at any particular instant in time If the direction is removed, it becomes Instantaneous Speed The slope of a line on a position/time plot is the average velocity

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Limit Calculation Eventually the calculation ceases to change This is then the slope of a tangent to the curve

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The Derivative Taking a Derivative is the same as calculating the Limit The Derivative of the equation gives an equation for the slope of any tangent

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The Position Function The Derivative of the position function is the Instantaneous Velocity

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Sample Problem 2-2 Plot Velocity vs. Time by analyzing Position vs. Time Break the x(t) plot into three segments The slope of the line is the velocity

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Go Backwards The displacement of the elevator? The Area under the curve is displacement Integrating the Function yields displacement

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Check Your Understanding Work through Sample Problem 2-3 –An example of derivation and calculating instantaneous velocity CHECKPOINT 3 –Which function shows constant velocity? –Which shows negative velocity?

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Average Acceleration Rate of change of velocity

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Instantaneous Acceleration Acceleration at any particular instant in time

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Col. J. P. Strapp Accelerated to 1020 km/h (634 mi/h) –Photos 1 and 2 Quickly Stopped!! –Photos 3 through 6 –Problem 30E What a Nut!!

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Comparing Directions Problem Solving Tactic, page 18 If velocity and acceleration have the same sign, then what is happening to the speed? What do opposite signs indicate?

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Sample Problem 2-4 Let’s take a close look

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Acceleration (a vector quantity) is defined as the rate of change of velocity. It has units of m/s 2 Acceleration can be positive, negative, or zero. An.

Acceleration (a vector quantity) is defined as the rate of change of velocity. It has units of m/s 2 Acceleration can be positive, negative, or zero. An.

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