V=distance divided by time
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There are different formulae for calculating these variables which depend on what information is available.
The Laplace equation is used commonly in two situations. It is used to find fluid flow and in calculating electrostatics.
Linear mass density, u, can be calculated by isolating the u variable in the following equation: v = √(F/u), where v is the velocity, F is the force of tension, and u is linear mass density. Therefore, the equation would be: u = F/v2. You may need to first solve for velocity, using the equation v = fλ, where f is frequency and is λ wavelength. You may also need to solve for force of tension before solving for u. You can use the equation F = mass x gravity, where mass is in kilograms and gravity is 9.8 m/s2. After calculating these variables, you can calculate linear mass density by plugging them into this equation: u = F/v2.
v1 = initial velocity v2 = final velocity
The quadratic equation is used to find the intercepts of a function (F(x)=x^(2*n), n being an even number) along its primary axis (typically the x axis). Many equations follow this form. The information given by the quadratic equation depends on what your function is pertaining to. If say you have a velocity vs time graph, when the function crosses the xaxis your particle has changed from a positive velocity to a negative velocity. This information can be useful to determine the accompanying behavior of your position. The quadratic equation is simply a tool to find intercepts of a function.