Further improve and make it gradually speed up with no collision to the effects and further improve:

```
--[[ 
    Advanced Flash Acceleration System
    Complexity Level: High
    Architecture: Multi-threaded Performance
    © Neural Dynamic Solutions
--]]

local Players = game:GetService("Players")
local RunService = game:GetService("RunService")
local UserInputService = game:GetService("UserInputService")
local TweenService = game:GetService("TweenService")
local ReplicatedStorage = game:GetService("ReplicatedStorage")

-- Configuration Matrix
local ACCELERATION_PARAMETERS = {
    BASE_SPEED = 50,
    ACCELERATION_COEFFICIENT = 1.75,
    MOMENTUM_THRESHOLD = 0.85,
    VELOCITY_DAMPENING = 0.92,
    FLASH_BURST_MULTIPLIER = 2.25,
    ENERGY_DECAY_RATE = 0.15,
    RECOVERY_INTERVAL = 0.45
}

-- Dynamic Speed Calculation System
local function calculateDynamicVelocity(baseVelocity, accelerationTime)
    local velocityMatrix = {}
    local currentVelocity = baseVelocity
    
    for i = 1, 10 do
        currentVelocity = currentVelocity * ACCELERATION_PARAMETERS.ACCELERATION_COEFFICIENT
        velocityMatrix[i] = currentVelocity * math.sin(accelerationTime * math.pi/2)
    end
    
    return velocityMatrix
end

-- Advanced Flash Movement Handler
local FlashMovementSystem = {}
FlashMovementSystem.__index = FlashMovementSystem

function FlashMovementSystem.new(character)
    local self = setmetatable({}, FlashMovementSystem)
    self.character = character
    self.humanoid = character:WaitForChild("Humanoid")
    self.rootPart = character:WaitForChild("HumanoidRootPart")
    self.energyReserve = 100
    self.isFlashing = false
    self.lastFlashTime = 0
    return self
end

function FlashMovementSystem:InitializeSpeedSystem()
    local speedModifier = Instance.new("NumberValue")
    speedModifier.Name = "SpeedModifier"
    speedModifier.Value = ACCELERATION_PARAMETERS.BASE_SPEED
    speedModifier.Parent = self.character
    
    return speedModifier
end

function FlashMovementSystem:ApplyVelocityTransformation(velocity, direction)
    local transformedVelocity = velocity * direction
    local dampening = ACCELERATION_PARAMETERS.VELOCITY_DAMPENING
    
    return Vector3.new(
        transformedVelocity.X * dampening,
        transformedVelocity.Y,
        transformedVelocity.Z * dampening
    )
end

function FlashMovementSystem:ExecuteFlashBurst()
    if self.energyReserve < 20 then return end
    
    local currentTime = tick()
    if currentTime - self.lastFlashTime < ACCELERATION_PARAMETERS.RECOVERY_INTERVAL then
        return
    end
    
    self.isFlashing = true
    self.lastFlashTime = currentTime
    
    local flashDuration = 1.5
    local initialPosition = self.rootPart.Position
    
    local velocityMatrix = calculateDynamicVelocity(
        ACCELERATION_PARAMETERS.BASE_SPEED,
        currentTime
    )
    
    spawn(function()
        for _, velocity in ipairs(velocityMatrix) do
            if self.humanoid.MoveDirection.Magnitude > 0 then
                local transformedVelocity = self:ApplyVelocityTransformation(
                    velocity,
                    self.humanoid.MoveDirection
                )
                
                self.rootPart.Velocity = transformedVelocity
                self.energyReserve = math.max(
                    0,
                    self.energyReserve - ACCELERATION_PARAMETERS.ENERGY_DECAY_RATE
                )
                
                -- Visual Effects System
                local flashEffect = Instance.new("Part")
                flashEffect.Size = Vector3.new(1, 1, 1)
                flashEffect.Transparency = 0.5
                flashEffect.CFrame = self.rootPart.CFrame
                flashEffect.Parent = workspace
                
                local tweenInfo = TweenInfo.new(0.3, Enum.EasingStyle.Quad, Enum.EasingDirection.Out)
                local tween = TweenService:Create(flashEffect, tweenInfo, {
                    Transparency = 1,
                    Size = Vector3.new(3, 3, 3)
                })
                tween:Play()
                
                game.Debris:AddItem(flashEffect, 0.3)
            end
            wait(0.1)
        end
        self.isFlashing = false
    end)
end

-- Energy Regeneration System
local function initializeEnergyRegeneration(flashSystem)
    spawn(function()
        while true do
            if not flashSystem.isFlashing and flashSystem.energyReserve < 100 then
                flashSystem.energyReserve = math.min(
                    100,
                    flashSystem.energyReserve + 1
                )
            end
            wait(0.2)
        end
    end)
end

-- Main Initialization
local function initializeFlashSystem(player)
    local character = player.Character or player.CharacterAdded:Wait()
    local flashSystem = FlashMovementSystem.new(character)
    local speedModifier = flashSystem:InitializeSpeedSystem()
    
    initializeEnergyRegeneration(flashSystem)
    
    -- Input Handler
    UserInputService.InputBegan:Connect(function(input, gameProcessed)
        if gameProcessed then return end
        
        if input.KeyCode == Enum.KeyCode.LeftShift then
            flashSystem:ExecuteFlashBurst()
        end
    end)
    
    -- Update Loop
    RunService.Heartbeat:Connect(function(deltaTime)
        if flashSystem.isFlashing then
            speedModifier.Value = ACCELERATION_PARAMETERS.BASE_SPEED * 
                ACCELERATION_PARAMETERS.FLASH_BURST_MULTIPLIER
        else
            speedModifier.Value = ACCELERATION_PARAMETERS.BASE_SPEED
        end
    end)
end

-- Player Connection Handler
Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function()
        initializeFlashSystem(player)
    end)
end)

-- Initialize Existing Players
for _, player in ipairs(Players:GetPlayers()) do
    if player.Character then
        initializeFlashSystem(player)
    end
end