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An object travels along a straight line. The function $s(t) = -4t^5 + 10t^4 + 7t^3 + t + 11$ gives the object's position, in meters, at time $t$ seconds. $\newline$ Write a function that gives the object's velocity $v(t)$ in meters 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) = -4t^5 + 10t^4 + 7t^3 + t + 11

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

t

seconds.

\newline

Write a function that gives the object's velocity

v(t)

in meters 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 $t$ .
Derivatives of terms: Differentiate each term of $s(t)$ separately: $\newline$ - The derivative of $-4t^5$ is $-20t^4$ . $\newline$ - The derivative of $10t^4$ is $40t^3$ . $\newline$ - The derivative of $7t^3$ is $21t^2$ . $\newline$ - The derivative of $t$ is $1$ . $\newline$ - The derivative of $11$ is $-4t^5$ $0$ , since it's a constant.

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