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An object travels along a straight line. The function $v(t) = -13t^3 - 2t^2 + 8t + 9$ gives the object's velocity, in feet per second, at time $t$ seconds. Write a function that gives the object's acceleration $a(t)$ in feet per second per second. $\newline$ a(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

v(t) = -13t^3 - 2t^2 + 8t + 9

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

t

seconds. Write a function that gives the object's acceleration

a(t)

in feet per second per second.

\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 $t$ .
Sum acceleration terms: Summing these differentiated terms gives us the acceleration function $a(t)$ .

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