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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 ?

Respuesta :

Space

Answer:

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

Step-by-step 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

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