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

Hi Chris,

The instantaneous velocity at time t = 0.2 is estimated by computing the average velocity between times t = 0 and t = 0.2.

We compute this using the formula (s(0.2) - s(0)) / (0.2 - 0)

= (0.45 - 0) / 0.2

= 2.25 ft/s.

I hope this is helpful! Contact me for more help if you are interested!