Four lab groups each choose a different time interval to estimate an object’s…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Four lab groups each choose a different time interval to estimate an object’s velocity at t=5.0 st=5.0\,\text{s} from position data collected during the motion. Group I:   4.0 s\;4.0\,\text{s} to 6.0 s6.0\,\text{s} Group II:   4.5 s\;4.5\,\text{s} to 5.5 s5.5\,\text{s} Group III:   4.9 s\;4.9\,\text{s} to 5.1 s5.1\,\text{s} Group IV:   5.0 s\;5.0\,\text{s} to 5.2 s5.2\,\text{s} Assuming the object is accelerating, which group’s choice is expected to yield the smallest error in estimating the velocity at 5.0 s5.0\,\text{s}? (a) Group I (b) Group III (c) Group II (d) Group IV

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