Question

T (sec) 0.0 - 0.5 - 1.0 - 1.5 - 2.0 - 2.5 - 3.0 - 3.5 - 4.0

s (ft) 12.5 - 26 - 36.5 - 44 - 48.5 - 50 - 48.5 - 44 - 36.5
Assuming that this smooth curve represents the motion of the body, estimate the velocity at t = 1.0, t = 2.5, and t = 3.5.

Answer 1

Well let me help you here. My suggestion is that you use your favorite technique to find a smooth curve that fits the data points
reasonably well. Lets remember that the t values are equally spaced, I'd use Newton's forward difference formula
It tells you that s(t) = 12.5 + 30t - 6t², and this fits the data perfectly.
So s'(t) = 30 - 12t,
Apply what im telling you and yu will get to the result