Example Notebook, Kinematics

Position vs. time.

Show[
Plot[
Piecewise[
{{1+2(((t-0))^2),0≤t≤2},
{9+8(t-2)-2(((t-2))^2),2≤t≤6},
{9-8(t-6)+1(((t-6))^2),6≤t≤10},
{-7,10≤t≤12}}
],
{t,0,12},
PlotRange->{{0,12},{-10,20}},
Exclusions->None,
PlotStyle->{Orange,Thick},
Frame->True,
FrameLabel->{ t[seconds],x[meters]},
GridLines->{{2,4,6,8,10},{ -5,5,10,15}},
GridLinesStyle->Directive[LightBlue,AbsoluteThickness[1.3]],
ImageSize->600,
AspectRatio->0.35,
LabelStyle->(FontSize->12)
]
]

Velocity vs. time.

Show[
Plot[
Piecewise[
{{4(t-0),0≤t≤2},
{8-4(t-2),2≤t≤6},
{-8+2(t-6),6≤t≤10},
{0,10≤t≤12}}
],
{t,0,12},
PlotRange->{{0,12},{-10,10}},
Exclusions->None,
PlotStyle->{Blue,Thick},
Frame->True,
FrameLabel->{ t[seconds],v[meters per second]},
GridLines->{{2,4,6,8,10},{ -5,5}},
GridLinesStyle->Directive[LightBlue,AbsoluteThickness[1.3]],
ImageSize->600,
AspectRatio->0.35,
LabelStyle->(FontSize->12)
]
]

Acceleration vs. time.

Show[
Plot[
Piecewise[
{{4,0≤t≤2},
{-4,2≤t≤6},
{2,6≤t≤10},
{0,10≤t≤12}}
],
{t,0,12},
PlotRange->{{0,12},{-5,5}},
PlotStyle->{Red,Thick},
Frame->True,
FrameLabel->{ t[seconds],a[meters per second second]},
ImageSize->600,
AspectRatio->0.35,
LabelStyle->(FontSize->12)
],
ListPlot[{{2,4},{2,-4}},Joined->True,PlotStyle->{Red,Dashed}],
ListPlot[{{6,-4},{6,2}},Joined->True,PlotStyle->{Red,Dashed}],
ListPlot[{{10,2},{10,0}},Joined->True,PlotStyle->{Red,Dashed}]
]