25% part (c) assume that d is the distance the cheetah is away from the gazelle when it reaches full speed. derive an expression in terms of the variables d, vcmax and vg for the time, tc, it takes the cheetah to catch the gazelle.

maximum speed of cheetah is

speed of gazelle is given as

Now the relative speed of Cheetah with respect to Gazelle

now the relative distance between Cheetah and Gazelle is given initially as "d"

now the time taken by Cheetah to catch the Gazelle is given as

so by rearranging the terms we can say

so above is the relation between all given variable