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An object travels along a straight line. The function $s(t) = 3t^{\frac{4}{3}} + 6t^{\frac{1}{3}}$ gives the object's position, in feet, at time $t$ minutes. $\newline$ Write a function that gives the object's velocity $v(t)$ in feet per minute. $\newline$ $v(t) =$ ______

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

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

s(t) = 3t^{\frac{4}{3}} + 6t^{\frac{1}{3}}

gives the object's position, in feet, at time

t

minutes.

\newline

Write a function that gives the object's velocity

v(t)

in feet per minute.

\newline

v(t) =

______

Differentiate position function: To find the velocity function $v(t)$ , we need to differentiate the position function $s(t)$ with respect to time $t$ .
Combine terms for velocity: Combine the differentiated terms to form the velocity function $v(t)$ .

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