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
Limit Calculation Eventually the calculation ceases to change This is then the slope of a tangent to the curve
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
The Position Function The Derivative of the position function is the Instantaneous Velocity
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
Go Backwards The displacement of the elevator? The Area under the curve is displacement Integrating the Function yields displacement
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?
Average Acceleration Rate of change of velocity
Instantaneous Acceleration Acceleration at any particular instant in time
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!!
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?