Label: left parenthesis, 0 , negative 9.8 1 , right parenthesis0,−9.81
Label:
7
Label: left parenthesis, 77.6 , 0 , right parenthesis77.6,0
Label:
8
`a\left(t\right)=-g\operatorname{sech}^{2}\left(\operatorname{arctanh}\left(v_{0}\sqrt{\frac{k}{mg}}\right)-t\sqrt{\frac{kg}{m}}\right)\left\{t\ge0\right\}` left parenthesis, 68.2 , negative 1.5 6 , right parenthesis68.2,−1.56
Label:
9
10
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left parenthesis, 0 , negative 9.8 1 , right parenthesis0,−9.81
left parenthesis, 77.6 , 0 , right parenthesis77.6,0
"a" left parenthesis, "t" , right parenthesis equals negative "g" hyperbolic secant squared left parenthesis, arctanh left parenthesis, "v" Subscript, 0 , Baseline StartRoot, StartFraction, "k" Over "m" "g" , EndFraction , EndRoot , right parenthesis minus "t" StartRoot, StartFraction, "k" "g" Over "m" , EndFraction , EndRoot , right parenthesis left brace, "t" greater than or equal to 0 , right braceat=−gsech2arctanhv0kmg−tkgmt≥0