An object travels along a straight line. The function v(t) = 4t^4 - 3t^3 - 11t + 3 gives the object's velocity, in feet per hour, at time t hours. Write a function that gives the object's acceleration a(t) in feet per hour per hour. a(t) = ______

Identify Velocity Function: Identify the velocity function and the need to differentiate it to find acceleration. The velocity function v(t) = 4t^4 - 3t^3 - 11t + 3 needs to be differentiated to find the acceleration function a(t). Differentiate each term of v(t) with respect to t.Differentiate 4t^4: Differentiate the first term 4t^4. Using the power rule, the derivative of 4t^4 is 16t^3.Differentiate -3t^3: Differentiate the second term -3t^3. Using the power rule, the derivative of -3t^3 is -9t^2.Differentiate -11t: Differentiate the third term -11t. Using the power rule, the derivative of -11t is -11.Differentiate Constant Term: Differentiate the constant term +3. The derivative of a constant is 0.Combine Differentiated Terms: Combine all the differentiated terms to form the acceleration function. a(t) = 16t^3 - 9t^2 - 11 + 0 Simplify to a(t) = 16t^3 - 9t^2 - 11.

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An object travels along a straight line. The function $v(t) = 4t^4 - 3t^3 - 11t + 3$ gives the object's velocity, in feet per hour, at time $t$ hours. $\newline$ Write a function that gives the object's acceleration $a(t)$ in feet per hour per hour. $\newline$ a(t) = ______

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Calculus

Relate position, velocity, speed, and acceleration using derivatives

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Q. An object travels along a straight line. The function

v(t) = 4t^4 - 3t^3 - 11t + 3

gives the object's velocity, in feet per hour, at time

t

hours.

\newline

Write a function that gives the object's acceleration

a(t)

in feet per hour per hour.

\newline

a(t) = ______

Identify Velocity Function: Identify the velocity function and the need to differentiate it to find acceleration. $\newline$ The velocity function $v(t) = 4t^4 - 3t^3 - 11t + 3$ needs to be differentiated to find the acceleration function $a(t)$ . $\newline$ Differentiate each term of $v(t)$ with respect to $t$ .
Differentiate $4t^4$ : Differentiate the first term $4t^4$ . Using the power rule, the derivative of $4t^4$ is $16t^3$ .
Differentiate $-3t^3$ : Differentiate the second term $-3t^3$ . Using the power rule, the derivative of $-3t^3$ is $-9t^2$ .
Differentiate $-11t$ : Differentiate the third term $-11t$ . Using the power rule, the derivative of $-11t$ is $-11$ .
Differentiate Constant Term: Differentiate the constant term $+3$ . The derivative of a constant is $0$ .
Combine Differentiated Terms: Combine all the differentiated terms to form the acceleration function. $\newline$ $a(t) = 16t^3 - 9t^2 - 11 + 0$ $\newline$ Simplify to $a(t) = 16t^3 - 9t^2 - 11$ .