1. Using the Derivative AP Physics C Mrs. Coyle http://www.ima.umn.edu/~arnold/graphics.html

2. Instantaneous Velocity v = lim  x   t  0   t v = dx  dt or

3. Instantaneous Acceleration or a = lim  v   t  0   t a = dv  dt

4. Using the limit to calculate instantaneous acceleration. Example 1: The velocity of a particle is given by v= -t 2 + 2 (t is in sec). Find the instantaneous acceleration at t= 4s (using the limit). Answer: -8 m/s

5. Evaluating the derivative of a polynomial. For y(x) = ax n dy = a n x n-1 dx -Apply to each term of the polynomial. -Note that the derivative of constant is 0.

6. Using the derivative to calculate instantaneous acceleration. Example 2: The velocity of a particle is given by v= -t 2 + 2 (t is in sec). Find the instantaneous acceleration at t= 4s (using the derivative). Answer: -8 m/s

7. Example 3: A particle’s position is given by the expression x= 4-t 2 + 2t 3 (t is in sec). Find for t= 5s : a)Its position b)Its velocity c)Its acceleration Answer: a) 229m, b) 140 m/s, c) 58 m/s 2

8. Example 4 An object follows the equation of motion x= 3t 2 -10t +5. a) At what time(s) is its position equal to zero? b) At what time is its velocity equal to zero? Hint: Remember for a quadratic equation ax² + bx + c = 0, the roots are: Answer: a) 0.62sec and 2.7sec, b) 1.7sec