Chapter 1, Section 1:  Activity 1.1.2

a. Compute the average velocity of the ball on each of the following time intervals:.... Include units for each value.

s[t_]:=64-16(t-1)^2
neighbors={.4,.7,.79,.799,.801,.81,.9,1.2};
pts=Table[{t,0.8},{t,{.4,.7,.79,.799,.801,.81,.9,1.2}}];
slopes=Table[{t,(s[t]-s[0.8])/(t-0.8)},{t,neighbors}];
MatrixForm[slopes]
ListPlot[slopes]

p1=Plot[s[t],{t,0,1.2}];
points=Table[{t,s[t]},{t,neighbors}];
p2=ListPlot[points,PlotStyle->PointSize[Large]];
p3=Plot[(s[0.4]-s[0.8])/(0.4-0.8)(x-0.8)+s[0.8],{x,0,1.2}];
Show[p1,p2,p3,PlotLabel->"The Neighbors of 0.8",AxesLabel->{"Time (s)","Height (ft)"},AspectRatio->1]

Manipulate[
m=(s[0.8]-s[0.8-h])/(h);
Show[
Plot[s[x],{x,0.8-h,0.8+h},PlotLabel->m],
Plot[(s[0.8]-s[0.8-h])/(h)(x-0.8)+s[0.8],{x,0.8-h,0.8+h},PlotStyle->Red],
ListPlot[{{0.8,s[0.8]},{0.8-h,s[0.8-h]},{0.8+h,s[0.8+h]}},PlotStyle->PointSize[Large]]
],
{{h,0.5},0.001,1,0.001}
]