Answer
The required linear function which matches the given data is $v(t)=9.7t+39.2$ m/s.
Work Step by Step
Let the required function be $v(t)=m\cdot t + c$.
Now, using data we have $v(0)=39.2$ m/s and $v(2)=58.6$, so, we get $39.2=m(0)+c$ and $58.6=2m+c$.
The first equation simplifies to $c=39.2$ and substituting this value in second equation gives $58.6=2m+39.2$, or, $2m=19.4$, or, $m=9.7$.
Therefore, the required function is $v(t)=9.7\cdot t +39.2$ m/s.
