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

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?

danjs · Answer

did you learn that the velocity function is the derivative of the position function

danjs · Answer

average velocity = displacement / time

= [s(e) - s(1)] / (e - 1)

danjs · Answer

ln(e) = 1
ln(1) = 0

danjs · Answer

e - 1 = about 1.72 seconds

danjs · Answer

Average velocit, secant line connecting 2 points on the graph of position vs time, is in this case

<v> = 1 / 1.72 or about 0.581 feet per second

danjs · Answer

slope of secant line*