Я бы добавил переменную PowerUp (BoolValue) для каждого игрока, который присоединяется к игре:
-- Add a "PowerUp" variable to every player that joins the game
game.Players.PlayerAdded:Connect(function(player)
local powerUp = Instance.new("BoolValue", player)
powerUp.Name = "PowerUp"
end)
-- Set "PowerUp" to true, when player touches part
script.Parent.Touched:Connect(function(touchedPart)
local char = touchedPart.Parent
local player = game.Players:GetPlayerFromCharacter(char)
if (player == nil) then return end
player.PowerUp.Value = true
end)