Example 2
Let \[\begin{array}{rl} g:[0,4\pi] & \rightarrow\mathbb{R}^{2}\\ t & \rightarrow\left(\cos\left(\frac{t}{2}\right),\,\sin\left(\frac{t}{2}\right)\right) \end{array}\]
Then \(g'=\left(-\frac{1}{2}\sin\left(\frac{t}{2}\right),\,\frac{1}{2}\cos\left(\frac{t}{2}\right)\right)\); \(v(t)=\left|g'(t)\right|=\frac{1}{2}\) and the trace of this curve is: