Hello everyone, Tom from everystepcalculus.com everystepphysics.com, a quick example of
vector valued function, r(t) formula, or vector function. And with regard to speed. So, let’s do it. Index 8 to get to my menu. We’re gonna scroll up to get to the bottom of the menu so that we’re closer to the s section; it’s all alphabetical. I choose speed. Speed is a scaler, meaning it has no direction, it has magnitude, but no direction. Unless time is added to it, and then it does have a direction. You’re gonna enter these values here, but if Z is not given you’re gonna enter 0, okay? So, you have to press alpha before you enter anything in these entry lines here. Alpha minus 3 times T Alpha 2 times T Alpha minus 6 times T. I always show you what you’ve entered, you can change it if you want. There’s the vector. These indicate that it’s a vector, these arrows here. Say it’s okay. Now we’re gonna choose speed, we’re looking for speed. It’s right there. And it’s given by the magnitude. Magnitude is the derivative of the function times the squares of each one of them. So it’s X prime of t squared, y prime of t squared, z prime of t squared. And the derivatives are minus 3, 2, and minus 6. And we square them. Asks if there’s time given, I’d say there’s no time given in this one. So we’re gonna choose number 2. And then just square the values, sum them up,
49, and there’s the answer: 7 units per second. Pretty neat, huh? everystepcalculus.com, go to my site, buy my programs, and subscribe if you want to see other videos. Have a good one.