Question

The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for e ≤ t ≤ 2e

Answer 1

The average rate of change of a continuous function \(f(x)\) over an interval \([a,b]\) is \(\dfrac{f(b)-f(a)}{b-a}\).

Velocity is a measure of the rate of change of the particle's position, so the average velocity for this particle will be \(\dfrac{s(2e)-s(e)}{2e-e}=\cdots\)

Answer 2

(Same average rate of change would be for the intervals
1. \(\color{black}{\left[a,b\right) }\)
2. \(\color{black}{\left(a,b\right] }\)
3. \(\color{black}{\left(a,b\right) }\)

Answer 3

just want to make a smile)