# Velocity

Let , be a parametric curve. The rate of change of the position is given by , and is called the velocity at , . The computer may help us understand the velocity by drawing the line segments joining with , as ranges over equally spaced points of the interval . For example, the velocity along the circle , , is represented as:

The procedure follows these steps in Maple:

 > x:=cos(t);  > y:=sin(t); > x1:=diff(x,t); > y1:=diff(y,t);  > xx:=x+x1;  > yy:=y+y1;  > m:=[[x,y],[xx,yy]];  > t:=2*n*Pi/100;  > plot([m\$n=1..100],color=black,axes=none);

The velocity along the epicycloid appears as:
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The velocity along the epicycloid appears as:
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The velocity along the cycloid appears as:
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