# 3 – Motion Models

Let’s take a closer look at the last example. The initial state of the car is at the zero meter position and it’s moving forward at a velocity of 50 meters per second. Let’s assume that our car keeps moving forward at a constant rate. Every second it moves 50 meters, so after three seconds it will have reached the 150 meter mark and its velocity will not have changed. That’s what a constant velocity means. It’s new predicted the state will be at the position 150 meters and with the velocity still equal to 50 meters per second. This is a reasonable prediction and we made it using just; one, the initial state of the car and two, an assumption that the car is moving at a constant velocity. This last assumption can be mathematically represented by the physics equation; distance traveled = velocity*time. This equation is also referred to as a motion model and there are many ways to model motion. This model assumes constant velocity. In our example, we’re moving at a constant velocity of 50 meters/second for three seconds and we formed our new position estimate with the constant velocity equation, 150 meters = 50 meters/second * 3 seconds. In order to predict where a car will be at a future point in time, you have to rely on a motion model. It’s important to note that no motion model is perfect. It’s a challenge to account for outside factors like wind or elevation or even things like tire slippage and other uncertainties. But these models are still very important for localization. Next, you’ll be asked to write a function that uses a motion model to predict a new state.