$[20$ points$]/$ have organized a race between a horse, a mouse with a jetpack, and a cheetah but he's depressed so he's not as fast as he usually would be$.$ The three animals start at $t=0$ and move along a line according to the following velocity functions:

$v_{\text{H}\text{o}\text{r}\text{s}\text{e}}=\frac{100}{2-t},v_{\text{M}\text{o}\text{u}\text{s}\text{e}}=\frac{-100}{(2-t{)}^2},v_{\text{C}\text{h}\text{e}\text{e}\text{t}\text{a}\text{h}}=\frac{100}{2-t^2}$

a$.$ Which animal is in the lead after $1$ second? In other words, which animal travels farthest on the interval $0t1?[5$ points$]$

b$.$ Which animal travels the farthest on the interval $0t5?$ As a note, the animals may end up going forward or backwards. Because they're animals, not professional racers. So a negative position is losing to a positive position. $[5$ points$]$

c$.$ Find the position functions, $s(t),$ for each animal assuming each animal starts at the origin.