And, just like with velocity, I will denote that by not putting a subscript. Or, you could think about the instantaneous acceleration. You could call that the velocity displacement vector, but I wouldn't recommend it. Quite equivalent to average velocity Or, you could write it like this. Here, we're going to have the final time minus the initial time. Instead of the displacement here, we're going to have the final velocity minus the initial velocity. You can do this avg, just like with average velocity. If you want to think about it over some interval, you can have the initial velocity at the beginning of the time interval and the final velocity at the end of the time interval. Now, in terms of definitions, we do have the two different kinds of acceleration, just like we have the two different kinds of velocity. It's in- the MKS unit is meters per second squared. It is, of course, a vector, because it is the change of a vector. Let's say, the object has acceleration, which, a more technical definition, is the rate of change of velocity with time. The only error in this plot, I would say, is the slope should be coming to zero at the origin. That's a quick plot of, basically, what it would look like. If we were to plot the acceleration versus time, near the surface of the Earth, the acceleration was constant. That's what it means to accelerate, in this case. At the beginning, when I released it, it had no velocity, and then, it would increase. If I were to plot v, the velocity, versus time, what would it do? Let's see. If it's speeding up, that slope has to increase. It falls farther and farther, with a higher and higher slope. We don't have the math, but for now, just trust me. In this case, I'll write down as positive. First, let's do a quick drawing to remind us.
If we want to, now, do our graphs and equations. Near the surface of the Earth, things accelerate as they fall down. If you want to demonstrate acceleration, you just drop something. But, usually, acceleration can mean either one. The plain spoken definition is when something speeds up or slows down, although, I guess, technically, that's deceleration. Our next concept to define is acceleration.
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