Question

The position of a particle on the x-axis at time t, t > 0, is s(t) = e^t with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 0 ≤ t ≤ In3?

3
2/ln3
3/ln3
3/2

Also please just tell me which on it is

Answer 1

0 ≤ t ≤ ln(3)

When t = 0
$s(0) = e^0 = 1$

when t = ln(3)
$s(ln(3)) = e^{ln3} = 3$

We have two coordinates: (0, 1) and (ln(3), 3)

The rate of change = The difference in y-coordinates ÷ the difference in x-coordinates

The rate of changes  = [3 - 1] ÷ [ln(3) - 0] = 2/ln(3)

Answer: 2/ln(3)