Simplified

--[[
	A much simplified version. The only problem with this is that wait(INTERVAL) is a blindspot.
	If the player stops during this time, and resumes really quickly,the speed won't reset.
--]]

local player = game.Players.LocalPlayer
local hum = player.Character:WaitForChild("Humanoid")

local WALK_SPEED = 16 -- Beginning walk speed
local INCREASE = 0.5 -- How much it accelerates each time
local INTERVAL = 0.1

while true do
	while hum.MoveDirection ~= Vector3.new() do -- While the humanoid hasn't stopped
		hum.WalkSpeed = hum.WalkSpeed + INCREASE
		wait(INTERVAL)
	end
	hum.WalkSpeed = WALK_SPEED
	-- Wait for player to start running agains
	hum.Running:Wait() -- or wait for hum.MoveDirection to change with hum:GetPropertyChangedSignal()
end