Distance, Velocity, Acceleration, and Rectilinear

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 1 ≤ t ≤ e?

Options:

1. 1
2. e
3. e - 1
4. 

Answer 1

s(t) = lnt = position at time t

s'(t) = velocity at time t = 1/t

Average velocity on the interval [1,e] = 1 / (e-1)∫_{(from 1 to e)}(1/t)dt

= (1 / (e-1))[lne - ln1) = (1 / (e-1)[1 - 0] = 1/(e - 1)