Find = io.read("*line") -- input [ 'initialvel' ] made by tom

KinematicsDeriv='No'
        Term1, Term2, Term3, Term4, Term5 = 'N/A', 'N/A', 'N/A', 'N/A', 'N/A'
FirstDervPosition, SecondDervVelocity, ThirdDervAcceleration ='N/A', 'N/A', 'N/A'
Acceleration= 30
AverVel, initialvel, AverSpeed = 'N/A', 'N/A', 'N/A'
FinalVel= 300
Time= 10 
    TimeUnit='S'
Displacement='N/A'
    DisplacementEquiDistance='No'
        DisplacementUnit='M'
Distance='N/A'
    DistanceUnit='M' 
Widget=0

local function solveinvelDeD() -- none 
    if Acceleration ~= 'N/A' and Displacement ~= 'N/A' and Time ~= 'N/A' and FinalVel ~= 'N/A' then 
        initialvel = FinalVel - Acceleration * Time
    elseif FinalVel == 'N/A' then
        initialvel = Displacement - (((Acceleration * Time^2)/2)/Time)
    end -- time 
   -- print(initialvel)
    if Acceleration ~= 'N/A' and Displacement ~= 'N/A' and Time == 'N/A' and FinalVel ~= 'N/A' then 
        initialvel = math.sqrt(FinalVel^2 - 2*Acceleration*Displacement)
    elseif FinalVel == 'N/A' then
        initialvel = 'N/A'
    end -- displacement
    if Acceleration ~= 'N/A' and Displacement == 'N/A' and Time ~= 'N/A' and FinalVel ~= 'N/A' and Distance ~= 'N/A' then 
        initialvel = FinalVel - Acceleration * Time 
    elseif FinalVel == 'N/A' then
        initialvel = Distance - (((Acceleration * Time^2)/2)/Time)
    end -- time (Distance)
    if Acceleration ~= 'N/A' and Displacement == 'N/A' and Time ~= 'N/A' and FinalVel ~= 'N/A' and Distance ~= 'N/A' then 
        initialvel = math.sqrt(FinalVel^2 - (2*Acceleration*Distance))
    elseif FinalVel == 'N/A' then
        initialvel = 'N/A'
    end -- displacement, Distance
   -- print(initialvel)
    if Acceleration ~= 'N/A' and Displacement == 'N/A' and Time ~= 'N/A' and FinalVel ~= 'N/A' and Distance == 'N/A' then 
        initialvel = FinalVel - Acceleration*Time
    elseif FinalVel == 'N/A' then
        initialvel = 'N/A'
    end  -- acceleration

    if Acceleration == 'N/A' then 
        initialvel = 'N/A'
    end   
    print("Initial Velocity is " .. tostring(initialvel))
end

local function solveinvelDnD() -- initila velocity   
    if initialvel == 'N/A' and Acceleration ~= 'N/A' and Time ~= 'N/A' and Displacement ~= 'N/A' and FinalVel ~= 'N/A' then
        initialvel = FinalVel - Acceleration * Time
    elseif FinalVel == 'N/A' then
        initialvel = ((Displacement - (Acceleration * .5 * (time^2)))/time)
    end -- time
    if initialvel == 'N/A' and Acceleration ~= 'N/A' and Time == 'N/A' and Displacement ~= 'N/A' and FinalVel ~= 'N/A' then
        initialvel = math.sqrt(FinalVel^2 - 2*Acceleration*Displacement)
    elseif FinalVel == 'N/A' then
        initialvel = 'N/A'
    end -- displacement , initialvel
    if initialvel == 'N/A' and Acceleration ~= 'N/A' and Time ~= 'N/A' and Displacement == 'N/A' and FinalVel ~= 'N/A' then
        initialvel = FinalVel - Acceleration*Time
    elseif FinalVel == 'N/A' then
        initialvel = 'N/A'
    end -- displacement, time, initialvel
    if initialvel == 'N/A' and Acceleration ~= 'N/A' and Time == 'N/A' and Displacement == 'N/A' and FinalVel ~= 'N/A' or FinalVel == 'N/A' then
        initialvel = 'N/A'
    end
    if Acceleration == 'N/A' then 
        initialvel = 'N/A'
    end 
    if initialvel ~= 'N/A' then 
        initialvel = initialvel
    end
    print("Initial Velocity is " .. tostring(initialvel))
end

if DisplacementEquiDistance == "Yes"  then
    solveinvelDeD()
elseif DisplacementEquiDistance == "No" then
    solveinvelDnD()
else
    print("ERROR")
end