In[68]:=
f[t_]:={t^2,t}
In[69]:=
v[t_]:=f'[t]
v[t]
Out[69]=
{2 t, 1}
In[70]:=
Clear[motion,tang,unittang]
motion=ParametricPlot[f[t],{t,-3,3}];
In[71]:=
tang=vectorPlot[Table[f[i],{i,-3,3}],Table[f'[i]+f[i],{i,-3,3}]];
In[72]:=
Show[motion,tang,AspectRatio->Automatic];
In[73]:=
T[t_]:=f'[t]/Sqrt[f'[t].f'[t]]
T[t]
Out[73]=
2 t 1
{--------------, --------------}
2 2
Sqrt[1 + 4 t ] Sqrt[1 + 4 t ]
In[74]:=
unittang=vectorPlot[Table[f[i],{i,-3,3}],Table[T[i]+f[i],{i,-3,3}]];
In[75]:=
Show[motion, unittang,AspectRatio->Automatic];
