A position function has the positions listed below.

Question

t 2 4 7 10 12
f(t) 34 98 155 205 271

Approximate the instantaneous velocity at t=5. show work.

Answer 1

If we assume a piecewise linear function then the velocity at t=5 is just (155-98)/(7-4) = 19

If you want a secant to average the speed from t=2 to t=7, you get (155-34)/(7-2) = 10.4

a quadratic approximation using the first 3 points yields

f(t) = -2.6t^2 + 47.6t - 50.8

and you can refine the approximation using your favorite interval.

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