#4a) UAM: Galilean Free Fall Model, y"=-g, v'=-g
var('t')
y=function('y',t)
show(desolve(diff(y,t,2)+32,y))
show(desolve(diff(y,t,2)+32,y,[0,10,100]))
p1=plot(desolve(diff(y,t,2)+32,y,[0,10,100]),0,2*100/32,color='red')
v=function('v',t)
show(desolve(diff(v,t,1)+32,v))
show(desolve(diff(v,t,1)+32,v,[0,100]))
p2=plot(desolve(diff(v,t,1)+32,v,[0,100]),0,2*100/32,color='green')
show(p1+p2)
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\newcommand{\Bold}[1]{\mathbf{#1}}k_{2} t - 16 \, t^{2} + k_{1}
\newcommand{\Bold}[1]{\mathbf{#1}}-16 \, t^{2} + 100 \, t + 10
\newcommand{\Bold}[1]{\mathbf{#1}}c - 32 \, t
\newcommand{\Bold}[1]{\mathbf{#1}}-32 \, t + 100

\newcommand{\Bold}[1]{\mathbf{#1}}k_{2} t - 16 \, t^{2} + k_{1}
\newcommand{\Bold}[1]{\mathbf{#1}}-16 \, t^{2} + 100 \, t + 10
\newcommand{\Bold}[1]{\mathbf{#1}}c - 32 \, t
\newcommand{\Bold}[1]{\mathbf{#1}}-32 \, t + 100

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