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An object travels along a straight line. The function $v(t) = - t^{\frac{1}{5}} + 2t^{-2}$ gives the object's velocity, in feet per minute, at time t > 0 minutes. $\newline$ Write a function that gives the object's acceleration $a(t)$ in feet per minute per minute. $\newline$ 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) = - t^{\frac{1}{5}} + 2t^{-2}

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

t > 0

minutes.

\newline

Write a function that gives the object's acceleration

a(t)

in feet per minute per minute.

\newline

a(t) = ______

Differentiate Power Rule: To find the acceleration function $a(t)$ , we need to differentiate the velocity function $v(t)$ with respect to time $t$ .
Differentiate $2t^{-2}$ : Differentiate each term of $v(t)$ separately. For the first term, $-t^{1/5}$ , use the power rule: $\frac{d}{dt}$ of $t^n = n*t^{n-1}$ . Here, $n = \frac{1}{5}$ .
Combine Derivatives: For the second term, $2t^{-2}$ , again use the power rule.
Find Acceleration Function: Combine the derivatives to get the acceleration function $a(t)$ .

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