How to make a Dig It–style hold bar (smooth movement)

Hi!
I’m trying to recreate the Dig It bar mechanic
What I need:

a horizontal player bar

when the button is held, the bar smoothly accelerates to the right

while holding, it keeps moving with inertia

when the button is released, the bar smoothly slows down and returns to the left, like gravity pulling it back

no tweens or teleporting, maybe physics (velocity, acceleration, dt)

Any advice or example logic would really help. Thanks!

The first idea I came up with involves using a frame that acts as the bar. You can set the anchor point to be on the left edge and use the UDim2 Lerp method in conjunction with the run service to make the bar grow gradually. All that’s left is figuring out a way to increase the alpha in the way that you want the bar to grow.