### Home > APCALC > Chapter 11 > Lesson 11.3.1 > Problem11-84

11-84.

An object is moving in a straight line such that its distance traveled after $t$ minutes is $s = –\ln( \frac { 1 } { t + 1 } )$ meters.

1. What is the object’s average velocity over $0 ≤ t ≤ 3$?

First, graph the equation and make sure the object does not change directions.
$\text{average velocity} = \left(\text{total distance}\right)/\left(\text{total time}\right)$

total distance $= s\left(3\right) - s\left(0\right)$

2. What is the acceleration of the object at $t = 2$ minutes?

$s\left(t\right) = \ln\left(t + 1\right)$

$a(2)=\frac{d^2}{dt^2}\ln(t+1)\Big|_{t=2}$