Answer:
A: The variation equation is [tex]D={\alpha}v^2.[/tex]
B: The speed is [tex]v=\sqrt{\frac{D}{\alpha } }[/tex]
Step-by-step explanation:
Part A:
The stopping distance is directly proportional to the square of the speed. Mathematically this means the distance [tex]D[/tex] is equal to the square of speed [tex]v[/tex] multiplied by a proportionality constant [tex]\alpha[/tex], thus
[tex]D={\alpha}v^2.[/tex]
Part B:
Once we have the equation relating [tex]D[/tex] and [tex]v[/tex], then it is easy to solve for [tex]v[/tex] using that equation.
Rearranging the equation we got in Part A and solving for [tex]v[/tex] we get:
[tex]v=\sqrt{\frac{D}{\alpha } }[/tex]
