http://code.coronalabs.com/code/object-moving-along-bezier-curve-example

main.lua

local bg = display.newImage("images/bg.png")
bg.x = _W/2; bg.y = _H/2; 
 
local car = display.newImage("images/car.png")
car.x = _W/2
car.y = _H - 250
car.name = "car"

-- understood proprierties of bezier curve
--local curve = bezier:curve({xInitial, xControlPoint1, xControlPoint2, xControlPoint3}, {yInitial, yControlPoint1, yControlPoint2, yControlPoint3})

local curve =  bezier:curve({150, 1100, 150},{ 1080, 686, 500})
local x1, y1 = curve(10.51)
local line3 = display.newLine(x1, y1, x1+1, y1+1)
line3:setColor(0, 0, 255, 255 )
line3.width = 3

for i=0.02, 1.01, 0.01 do
	local x, y = curve(i)
	line3:append(x, y)
	print(i, x, y)
end

-- move ball along curve
local pointInc = 0.00

local function follow (event )
	if pointInc < 1.01 then
        car.x, car.y = curve(pointInc)
		--print(pointInc,ball.x, ball.y)
        pointInc = pointInc + 0.01
     else
         Runtime:removeEventListener("enterFrame",follow)
     end
end

Runtime:addEventListener("enterFrame",follow);