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An object travels along a straight line. The function $s(t) = 10t - 3$ gives the object's position, in kilometers, at time $t > 0$ hours. $\newline$ Write a function that gives the object's velocity $v(t)$ in kilometers per hour. $\newline$ $v(t) = \underline{\hspace{3cm}}$

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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) = 10t - 3

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

t > 0

hours.

\newline

Write a function that gives the object's velocity

v(t)

in kilometers per hour.

\newline

v(t) = \underline{\hspace{3cm}}

Identify Position Function: Identify the position function and understand what is required. $\newline$ The position function $s(t) = 10t - 3$ describes how the position of the object changes with time. We need to find the velocity function, which is the derivative of the position function with respect to time.
Differentiate to Find Velocity: Differentiate the position function to find the velocity function. $\newline$ Differentiate $s(t) = 10t - 3$ with respect to $t$ to get $v(t)$ . $\newline$ Using the power rule, the derivative of $10t$ is $10$ , and the derivative of $-3$ is $0$ . $\newline$ So, $v(t) = 10$ .

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