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Well I’m starting at five meters per second. And this tells us the distance. So it might look something look something like that. So you’re going from times zero to time four, your change in time is four seconds. It’s the arithmetic mean of these two numbers. And just to make it clear with the numbers, these numbers really could be anything, I’m just picking these to make it concrete in your mind. So it’s just the area under this curve.
Eight meters per second. Easy to figure out the area of a triangle. That is my velocity right over there. How do I calculate its area?
Right now we have something in terms of time, distance, and average velocity but not in terms of initial velocity and acceleration.
Gennemsnitlig hastighed for konstant acceleration (video) | Khan Academy
So this right up here is 13 meters per second. What are the kinematic formulas? So this height right over here is eight meters per second.
What is the area? If I say it’s negative five meters per second, that means it’s five meters per second to the left. You can really view g as measuring the tifen field strength near the surface of the boilogi.
Average the two, and then multiply that times the time that goes by. And then every second that goes by, I’m going two meters per second faster.
That is the area of this right here.
This is the purple area, right over here. This is my final velocity. And I want to take a pause here.
Gennemsnitlig hastighed for konstant acceleration
Deriving displacement as a function of time, acceleration, and initial velocity. So this is the blue rectangle right over here.
Area of udgavr triangle is one half, times the base, which is four seconds, times the height, which is eight meters per second. Because it’s two meters per second, per second. Deriving max projectile displacement given time.
Deriving displacement as a function of time, acceleration, and initial velocity
We can assume these values right over here. Let me make sure that these are all vector quantities Tdien are going to leave it right over here. So if you go five meters per second, for four seconds, you’re going to go 20 meters. And then plus– what do we have to do– we have the change in time, once again, we have the change in time, times this height. So times one half. The base here is still biologo, because that’s five seconds have gone by.
The height here is my final velocity minus my initial velocity. I can draw a straighter line than that. And so this is v. So we can rewrite this expression as the initial velocity plus something over 2. You get distance is equal to change in time, times– factoring out the one half– v i plus v f. Gennemsnitlig hastighed for konstant acceleration. So I’m going to do it both, using the variables, and using the concrete numbers. How fast are we going after four seconds, and how far have we traveled over the course of those four seconds.
The other thing I want to make clear: If this was a curve or if the acceleration was changing, you could not do that. So we have five meters per second, plus four times two is eight. Now what I want to do is do this exact same calculation, but keep it in variable form and that’ll give another formula that many people, many often memorize.