Since you are using Unity, there is actually a free package that can help you animate things and is super easy to use.
It's called "DOTween" and can be found in the Unity Asset Store. It allows you to interpolate values over time. You can use the "shortcut" extension function like transform.DOMove() to interpolate properties of an object, or you can set up your own tweens that call your own functions. There are also many ease methods. You can make an object accelerate and/or decelerate over time.
I've also used this package to make some animations in my game. If you watch closely, you'll notice that when the cup moves, it starts fast and slows down when it is closer to the destination. This makes the animation look quick and also smooth at the same time.