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An object travels along a straight line. The function $s(t) = 3\cos t - 7e^t$ gives the object's position, in feet, at time $t$ seconds. $\newline$ Write a function that gives the object's velocity $v(t)$ in feet per second. $\newline$ 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) = 3\cos t - 7e^t

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

t

seconds.

\newline

Write a function that gives the object's velocity

v(t)

in feet per second.

\newline

v(t) = ______

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

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