In real life, objects move in different ways according to their nature. A train that moves on tracks without stopping will have an approximately constant speed. However, when a train arrives at the station where it should stop, it reduces its speed, braking gradually. The same thing happens when moving objects--objects do not usually move at one speed from one point to another. When a person lifts an object, the first effort is usually faster at the beginning than when it is reaching its final position, and more precision is required when it's near its final position.

Almost all working frameworks have different types of movement available to give your application transitions that feel predictable and natural to the user.

The evolution of the value we are "easing" over time is usually represented by Bezier curves. Some common examples are Ease In, which changes the value to be slower at first, Ease Out, which changes the value to be slower at the end, and Ease In-Out, which starts and ends at a slower pace than at its midpoint. You can find some examples at http://easings.net/. They will be very useful when it comes to detailing how an animation should behave. The development team will normally have the means to include these types of curves in their projects, as they are widely supported by different development environments.