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An object travels along a straight line. The function $v(t) = 2\sqrt{t} - 6\sqrt[3]{t}$ gives the object's velocity, in meters per second, at time $t$ seconds. $\newline$ Write a function that gives the object's acceleration $a(t)$ in meters per second per second. $\newline$ a(t) = ______

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Relate position, velocity, speed, and acceleration using derivatives

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

v(t) = 2\sqrt{t} - 6\sqrt[3]{t}

gives the object's velocity, in meters per second, at time

t

seconds.

\newline

Write a function that gives the object's acceleration

a(t)

in meters per second per second.

\newline

a(t) = ______

Identify velocity function: Identify the velocity function and recognize the need to differentiate it to find acceleration. $\newline$ $v(t) = 2\sqrt{t} - 6\sqrt[3]{t}$ $\newline$ We need to differentiate $v(t)$ to find $a(t)$ , the acceleration function.
Differentiate each term: Differentiate each term of $v(t)$ separately. $\newline$ For the first term, $2\sqrt{t}$ , the derivative is $2 \times (1/2) \times t^{-1/2} = t^{-1/2}$ . $\newline$ For the second term, $-6\sqrt[3]{t}$ , the derivative is $-6\sqrt[3]{},$ since the derivative of $t$ with respect to $t$ is $1$ .

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\newline

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