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So for the first segment
\[ \vec{f_1}(t)=(2t,t) \]

so the second is (t,4t) right?

Then the full function is just
\[ \vec{f}(t)=
\begin{cases}
\vec{f_1}(t) & \text{if } 0≤t≤1 \\
\vec{f_2}(t) & \text{if } 1

ar.....sorry dude I don't really get it
can u give me a final answer
i will figure it out myself

thanks i will try to figure it out

Here is a picture I think will help a lot, if you think visually
|dw:1348317929963:dw|

I got the lines equations by finding t in terms of x or y in the parametrizations