Velocity

Let $[x(t),y(t)]$ , $t\in [a,b]$ be a parametric curve. The rate of change of the position $[x(t),y(t)]$ is given by $[x^{\prime }(t)$, $y^{\prime }(t)] $ and is called the velocity at $[x(t)$, $y(t)]$. The computer may help us understand the velocity by drawing the line segments joining $[x(t),y(t)]$ with MATH, MATH as $t$ ranges over equally spaced points of the interval $[a,b]$. For example, the velocity along the circle $[\cos \ t$, $\sin \ t]$, $t\in [0,2\pi ]$ 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 MATH appears as:
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The velocity along the epicycloid MATH appears as:
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The velocity along the cycloid MATHappears as:
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