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An object travels along a straight line. The function $v(t) = 3\sqrt{t} - 4t^2 + t$ 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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Relate position, velocity, speed, and acceleration using derivatives

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

v(t) = 3\sqrt{t} - 4t^2 + t

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) = ______

Differentiate velocity function: To find the acceleration function $a(t)$ , we need to differentiate the velocity function $v(t)$ with respect to time $t$ .
Combine derivatives for acceleration: Combine the derivatives to form the acceleration function $a(t)$ .

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\newline

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