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?

imnotarobot5 · Answer

So i know this question is similar to the other one, but I dont know what to do with the intervals?

danjs · Answer

The average velocity over an interval [a,b] is the slope of a line connecting the endpoints
$$ave.~~velocity=\frac{ change~\in~position }{ change~\in~time }=\frac{ s(b)-s(a) }{ b-a }$$

danjs · Answer

s(t)=ln(t)

for time interval  t =[1 , e]

$$ave~velocity=\frac{ \ln(e)-\ln(1) }{ e-1 }\approx$$

imnotarobot5 · Answer

so no derivatives need to be found?

danjs · Answer

not for this one, don't need velocity or acceleration functions.

imnotarobot5 · Answer

but is there a next step?