LESSON 57 – RATES OF CHANGE IN PHYSICSOctober 17, 2013
Fernando Morales, Human Being
Calculus!
SECOND DERIVATIVE
Differentiation of the first derivative of the function
Notations:
y’’ f ’’(x).
EXAMPLE #1
Determine f ’’(3)
f(x) = (3x2 + 2)-1/2(1-x)
Step 1: Find f ’(x)Step 2: Differentiate f ’(x) to get f ’’(x)Step 3: Replace x with 3 to get f ’’(3)
DISPLACEMENT, VELOCITY, AND ACCELERATION
Think of a position function/graph (displacement vs. time), s(t)
Derivative = Instantaneous rate of change = The gradient of a tangent line
Gradient: Rise/Run
DISPLACEMENT, VELOCITY, AND ACCELERATION
1st Derivative: Rise/Run -> Displacement/time->
units of m/s -> Velocity, s’(t) = v(t)
2nd Derivative: Rise/Run -> Velocity/time -> units
of m/s2 -> Accelerations’’(t) = a(t)
DISPLACEMENT, VELOCITY, AND ACCELERATION
VELOCITY & ACCELERATION
VELOCITY & ACCELERATION
Velocity Acceleration
Slope of Graph Motion
+ + Positive & Increasing
Speeding Up & Forward
+ - Positive & Decreasing
Slowing Down & Forward
- + Negative & Increasing
Slowing Down & Reverse
- - Negative & Decreasing
Speeding Up & Reverse
0 0 0 Stationary
FREEDOM QUESTION
REQUIRED BEFORE NEXT CLASS
McGraw Hill Section 2.3 # 7, 8, 9, 10, 16, 17
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