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And let’s say that we do this for a duration. I want to tide clear these are vector quantities. I’m going to call this the average velocity. And this tells us the distance.

You get distance is equal to change in time, times– factoring out the one half– v i plus v f. So this is my delta t. We have to take it by half because a triangle is only half of that rectangle.

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. Video udskrift The goal of this video is to explore some of the concepts, or formulas you might see in a traditional physics class.

And I want to take a pause here. So we can rewrite this expression as the initial velocity plus something over 2. And then after four seconds we will be at 13 meters per second.

In the next video we are going to use this formula we just derived. Well I’m starting at five meters per udgace. Or another way to think about it– let’s factor out this one half.


So v i is equal to five meters per second. After three seconds we will be 11 meters per second. Easy to figure out the area of a rectangle. But we have to be very careful with this. And I’m starting off at five meters per second.

Deriving displacement as a function of time, acceleration, and initial velocity

So you’re going from times zero to time four, your change in time is four seconds. Or I have tl constant slope here. You can break it down into this blue part, this rectangle right over here.

Well actually I want to plot displacement over time because that will be more interesting. After two seconds we will be at nine meters per second. And the change in velocity due to the acceleration.

And then every second that goes by, I’m going two meters udgxve second faster. Well the final velocity is going to be your initial velocity plus your acceleration times change in time.

Gennemsnitlig hastighed for konstant acceleration

Your average velocity is 9 meters per second, if you take the average of 13 and 5. So what is v i minus one half times v i. So it’s going to be plus, one half times v f, times our final velocity.


So this is the one half. The distance that we travelled. Or this is the same thing as 13 meters per second, which is going to be our final velocity. We can only calculate Vavg this way assuming constant acceleration. So, we have the acceleration due to gravity.

Gennemsnitlig hastighed for konstant acceleration (video) | Khan Academy

So I’ll be at seven. Once again when were are dealing with objects not too far from the center of the earth we can make that assumption. But the only reason why I can just take the starting velocity and the ending velocity and, adding them together, biologii then divide by two. Right now we have something in terms of time, distance, and average velocity but not in terms of initial velocity and acceleration. Essentially taking the average of these two things which would be someplace over here.