Answer
$v=4.3 \hspace{0.1cm} m/s$
Work Step by Step
Peak vertical force increases linearly with the pony's speed. Let force be denoted as $F $and speed be denoted as $v$. Then we can write the linear function in terms of $(v,F)$ as
$F=av+b$
Given two points satisfying this equation as $(2,0.75)$ & $(3,0.93)$.
Substituting these points in the above equation and solving we can find the values of a and b.
$0.75=2a+b\hspace{0.2cm} ... (1)$
$0.93=3a+b \hspace{0.2cm}...(2)$
subtracting equations $(1)$ and $(2)$ we get,
$a=0.18 $
$b=0.39$
Let's substitute the values of a and b in the function to get:
$F=0.18v+0.39 ... (3)$
At a critical force, the pony stops trotting and starts to gallop. Given the critical force as $F=1.16$.
At $F=1.16$, the speed will be $\frac{1.16-0.39}{0.18}=4.3\hspace{0.1cm} m/s$. (by substituting the value of $F$ in equation $(3)$)
