# 3 – Nd113 C6 L1 14 L A Typical Calculus Problem Part2 V2

In this typical problem, the vehicles position is given to you in terms of this nice algebraic expression, and the corresponding graph. And when you know the algebraic description of a function, like position, then there are all sorts of clever things you can do to calculate the derivative exactly. And by exact, I mean you can actually find another algebraic equation that gives you the derivative at any point. So for this function, the derivative winds up being -2T + 10, and that looks like this as a graph. And it’s actually pretty amazing that it’s possible to get an algebraic description of something like velocity from an algebraic description of position. But the problem is that in reality, when you’re dealing with a real car, navigating in the real world, you are never given this kind of description of motion. Nobody ever tells a self driving car, hey, your position for the next 10 seconds will be described by the following equation. In reality, what you’re going to get is data, and that data will come from your accelerometers, your odometers, your cameras, and LIDARs and radars, and it won’t necessarily be pretty. In the rest of the lesson, you’ll do exactly this, you’re going to work with odometer data to implement a speedometer and then an accelerometer.