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