4 – Nd113 C6 L2 03 L Acceleration Basics V2

Position, velocity, and acceleration are all related. And you’ve seen the velocity is the derivative of position, and acceleration is the derivative of velocity. Before we jump into calculus, it’s important to get a feel for what acceleration really means. And one way to do that is to look at the units associate with each of these quantities. Position, for example, might be measured in miles or kilometers. But most commonly, we’re going to use meters, which we abbreviate with a little m. And velocity is typically measured in units like kilometers per hour or miles per hour or again, more commonly, meters per second. But notice that each of these units has a unit of distance in the numerator and a unit of time in the denominator. And that’s because velocity is the derivative of distance traveled, it’s the rate of change of distance with respect to time. So what are the units associated with acceleration? Well, I already said it’s the rate of change of velocity with respect to time. So that means that the numerator should have units of velocity and the denominator should have units of time. And in fact, these are the units we’ll be using for acceleration. And when you see them written this way, you can read them as meters per second per second. Though often you’ll see them in this way, in which case it’s pronounced meters per second squared. And personally, I really prefer the first way of writing these units since it serves as a good reminder for what acceleration actually is. It’s the rate of change of velocity with respect to time. So that means acceleration just tells you how fast your velocity is changing.