$3\mathrm{.}14$ Piecewise functions are sometimes useful when the relationship between a dependent and an independent variable

cannot be adequately represented by a single equation. For

example, the velocity of a rocket might be described by

$10$t

$2$

$5$t $0<=$ t $<=8$

$6243$t $8<=$ t $<=16$

$\backslash$upsilon $($t$)=\{36$t $+12($t $16)2$

$16<=$ t $<=26$

$2136$e$0\mathrm{.}1($t$26)$ t $>26$

$0$ otherwise

Develop an M$-$file function to compute $\backslash$upsilon as a function of t$.$

Then, develop a script that uses this function to generate a

plot of $\backslash$upsilon versus t for t $=5$ to $50.$