Question

find the average velocity for the position function s(t) in mm over the interval 1<=t<=3 where t is in seconds t=0,1,2,3 and s(t)=9,4,9,14 ?

Answer 1

The average velocity between t=1 and t=3 seconds for the position function s(t) is calculated as the change in position over the change in time, which is 5 mm/s.

Step-by-step explanation:

To find the average velocity over the interval 1≤t≤3, where the position function s(t) is given for specific time points, you would need to calculate the change in position over the change in time within that interval. However, the position values provided are for t=0, 1, 2, 3 corresponding to s(t)=9, 4, 9, 14 mm respectively. Since we need to find the average velocity between t=1 and t=3 seconds, we take the value of s(3) - s(1) and divide it by the time interval (3-1 seconds).

Vavg = Δs / Δt

For the given data: Δs = s(3) - s(1) = 14 mm - 4 mm = 10 mm, and Δt = 3s - 1s = 2s.

Hence, the average velocity is Vavg = (10 mm) / (2 s) = 5 mm/s directed from position at t=1s to position at t=3s.