Estimating Velocity (Derivatives)

Question

I've been trying to work through this. I figured out the first half of this problem, but do not know how to estimate what the velocity at 0.2 would be.

Consider a car whose position, s, is given by the table

t (s) 0 0.2 0.4 0.6 0.8 1

s (ft) 0 0.45 1.7 3.8 6.5 9.6

1. Estimate the velocity at t=0.2.

Answer 1

Your best estimate for the instantaneous velocity is to take an average velocity over the smallest interval possible:

v_avg = (s(t2) - s(t1))/(t2-t1). You could do that from 0 to .2 s and .2 to .4 seconds. They will be different as the object seems to be accelerating. Because the time intervals are constant, you could average these velocities or take the average velocity from 0 to .4 seconds (Same result).

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