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An object travels along a straight line. The function $s(t) = t^2 - 10t + 12$ gives the object's position, in miles, at time $t$ hours. $\newline$ Write a function that gives the object's velocity $v(t)$ in miles per hour. $\newline$ 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) = t^2 - 10t + 12

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

t

hours.

\newline

Write a function that gives the object's velocity

v(t)

in miles per hour.

\newline

v(t) = ______

Differentiate position function: To find the velocity function $v(t)$ , we need to differentiate the position function $s(t) = t^2 - 10t + 12$ with respect to time $t$ .
Differentiate each term: Differentiating each term separately: $\newline$ The derivative of $t^2$ is $2t$ . $\newline$ The derivative of $-10t$ is $-10$ . $\newline$ The derivative of $12$ (a constant) is $0$ .
Combine to find velocity: Combining these, the velocity function $v(t) = 2t - 10$ .

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