How do I move the camera via script? Roblox lua

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Lua

I'm making a game in Roblox Studio where I need to set up a cut scene. So far, I've worked out the details about how to bring the camera to where I want the scene to occur, however right now, when it activates, the camera "teleport" to where it is. What I want is for the camera view to smoothly transition from the spawn to the cut scene.

What I have tried:

Here's the situation: I have a "camera" brick that is fully transparent, and is non collidable. It is positioned in a spot facing the cutscene, and a localscript utilizes this code:

local Player=game.Players.LocalPlayer
local Char=Player.Character or Player.CharacterAdded:Wait()
local camera=workspace.CurrentCamera

wait(0.5)
camera.CameraType=Enum.CameraType.Scriptable
camera.CFrame=workspace.CutsceneCam.CFrame
wait(11)
camera.CameraType=Enum.CameraType.Custom

This works well, by sending the camera viewport to the front face of the CutsceneCam part, however it just suddenly "moves" to the part from the current cam location - I need it to smoothly move there so the player's screen can see the camera moving to the cutscene location. Is there a way to accomplish this with script?