Question

an object travels along a straight line. the function $s(t) = 10t - 3 \ln t$ gives the objects position, in kilometers, at time $t > 0$ hours.
write a function that gives the objects velocity $v(t)$ in kilometers per hour.
$v(t) = $

Explanation:

Step1: Recall velocity is derivative of position

Velocity $v(t)$ is the first derivative of position function $s(t)$.

Step2: Differentiate each term of $s(t)$

For $10t$: derivative is $10$. For $-3\ln t$: derivative is $-3 \cdot \frac{1}{t}$.
Combine results: $v(t) = 10 - \frac{3}{t}$

Answer:

$v(t) = 10 - \frac{3}{t}$