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?

Question

a. 1

b.e

c. e-1

d. 1/e-1

Answer 1

Jacques, when I saw this problem, I assumed that it was the particle's velocity, not its position, that was given by ln t. So I integrated ln t to get t ln t - t, then substituted t = e and t = 1 to get e ln e - e - (1 ln 1 - 1) = e - e - (0 - 1) = 1. The amazing thing is, I get the same answer, even though I solved a completely different problem, one that actually does require calculus!

Answer 2

The average velocity for a time interval is simply (x(t₂) - x(t₁))/(t₂-t₁). In this case,

(ln(e)-ln(1))/(e-1) = 1/(e-1) I guess that's answer d, even though it is written incorrectly.

Please consider a tutor. Take care.