Question

An object moves along the x axis with its position x given as a function of time t by x(t) = Dt^2 - Ct + F

What is the object's velocity v as a function of time ?

Answer 1

v(t) = 2Dt - C

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Functions
• Function Notation

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Explanation:

Note: Velocity is the derivative of position

Step 1: Define

Identify

x(t) = Dt² - Ct + F

Step 2: Find Velocity

Differentiate

1. Basic Power Rule: x'(t) = 2Dt²⁻¹ - 1Ct¹⁻¹ + 0
2. Simplify: v(t) = 2Dt - C

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e