The data in Table 9.4 were collected with a motion detector and a CBL™ by Valerie Sharritts, then a mathematics teacher at St. Francis DeSales High School in Columbus, Ohio. The table shows the distance s (meters) coasted on inline skates in t sec by her daughter Ashley when she was 10 years old. Find a model for Ashley’s position given by the data in Table 9.4 in the form of Equation (2). Her initial velocity was ν₀ = 2.75 m/sec, her mass m = 39.92 kg (she weighed 88 lb), and her total coasting distance was 4.91 m.

TABLE 9.4 Ashley Sharritts skating data t (sec) t (sec) s (m) 0 3.05 0.16 3.22 0.32 3.38 0.48 3.52 0.64 3.67 0.80 3.82 3.96 4.08 4.18 4.31 4.41 4.52 4.63 4.69 0.96 1.12 1.28 1.44 1.60 1.76 1.92 2.08 s (m) 0 0.31 0.57 0.80 1.05 1.28 1.50 1.72 1.93 2.09 2.30 2.53 2.73 2.89 2.24 2.40 2.56 2.72 2.88 3.04 3.20 3.36 3.52 3.68 3.84 4.00 4.16 4.32 t (sec) 4.48 4.64 4.80 4.96 5.12 5.28 5.44 5.60 5.76 5.92 6.08 6.24 6.40 6.56 s (m) 4.77 4.82 4.84 4.86 4.88 4.89 4.90 4.90 4.91 4.90 4.91 4.90 4.91 4.91