Mathematics, 17.02.2021 03:50 amirasaleh1012

CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3. A. v(t) = sin(t) + cos(t) + 3
B. v(t) = sin(t) + cos(t) + 2
C. v(t) = sin(t) - cos(t) + 3
D. v(t) = sin(t) - cos(t) + 4

I picked A., which was marked wrong, although I truly believe that is the answer because I got sin(t) - (-cos(t)) + 3. Please tell me whether you believe this is right or am I doing something wrong. I really want to learn/master this concept. Thanks is advance.

CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t),

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Answer from: zoeybuch5

B. v(t) = sin(t) + cos(t) + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Function Notation

Calculus

Antiderivatives - Integrals

Integration Constant C

Solving Integration Equations

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Step-by-step explanation:

*Note: Remember that the velocity function is the integral of the acceleration function/acceleration is the derivative of velocity.

$\displaystyle v'(t) = a(t)\\v(t) = \int {a(t)} \, dt$

Step 1: Define

a(t) = cos(t) - sin(t)

v(0) = 3

Step 2: Integrate

Set up integral: $\displaystyle v(t) = \int {cos(t) - sin(t)} \, dt$ [integral] Rewrite [Integration Property - Subtraction]: $\displaystyle v(t) = \int {cos(t)} \, dt - \int {sin(t)} \, dt$ [Integral] Trig integration: $\displaystyle v(t) = sin(t) - [-cos(t)] + C$ [Velocity Integration] Simplify: $\displaystyle v(t) = sin(t) + cos(t) + C$

Step 3: Find Function

We need to solve for the entire function, meaning we need to find constant C.

Substitute in given point [Velocity Integration]: $\displaystyle v(0) = sin(0) + cos(0) + C$ [Velocity Integration] Substitute: $\displaystyle 3 = sin(0) + cos(0) + C$ [Velocity Integration] Evaluate trig: $\displaystyle 3 = 0 + 1 + C$ [Velocity Integration] Add: $\displaystyle 3 = 1 + C$ [Velocity Integration] Isolate C [Subtraction Property of Equality]: $\displaystyle 2 = C$ [Velocity Integration] Rewrite: $\displaystyle C = 2$ [Velocity Function] Substitute in C [Velocity Integration]: $\displaystyle v(t) = sin(t) + cos(t) + 2$

Topic: Calculus

Unit: Basic Integration

Book: College Calculus 10e

Answer from: Quest

the answer is 31.27mph

Answer from: Quest

it has changed from the width and the height.

step-by-step explanation:

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CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t),...