Question

At 0.100 s intervals, the x
coordinates of a particle are
0, 1.01 cm, 2.05 cm, and 3.12
cm. Estimate the
instantaneous velocity and
acceleration at t = 0.

Answer 1

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Answer 2

[f(.1)-f(0)]/.1 = .1
so, f'(0) is about .1

[f(.1)-f(0)]/.1 = .1
[f(.2)-f(.1)]/.1 = .5
so, f''(0) is about .4

looks like f(x) = 10x + x^2 + 4/3 x^3 ...