Hello everyone, Tom from everystepcalculus.com, everystepphysics.com, a problem dealing with parametric equations and the item of speed. So let’s do it! Index 8 to get to my menu, go to speed. Speed is a scaler, it has no direction, no angle, unless you add time to it, which I’ll show you in my program here. There’s speed, and write all this on your paper here, the r(t) formula is x(t)i, j, and k, and x, y, and z. And we have our functions for x and y. You have to press alpha before you enter anything into these entry lines here. Alpha… the problem is T cubed minus 4 times T. And Alpha T squared plus one. Looks like the “t” is missing. Here we go, put the “t” in. Here we go, and alpha 0 for the z component, or the K component if it’s not given. These are all set up problems, they don’t happen in real life,
which is nonsense for calculus. A lot of it is like that in calculus. So, I always show you what you’ve entered, you can change it if you want. Say it’s okay. And we’re gonna scroll down here to the calculation– you have different things on the menu that you can do with this entry of “t” variables. Speed, there it is there, and of course you write the derivative of the magnitude of it, which is actually the square of the derivatives. Calculus, the sudoku of math. X prime, here’s the derivatives of that and the magnitude is then the derivative squared. I’m going to say that the time was not given in this problem at first, so to do it we’re gonna go back, we’re gonna press number 2. And so speed is the square root of 3t squared plus 2t minus 4. We’re gonna go back and do it again. Add some time component. Press yes for time… add– yes, let’s put 7 seconds. And so, it’s t equals 7, you’re entering it into the variable of the function. You’re gonna put parenthesis around this “7” on your paper but I have to use quotation marks. Turns out to be that. Turns out to be 12.5 units per second. But, because “t” is given… “t” is given, so we do have an answer, it’s 1.4732, arc tangent of the rise over run. Have a good one, everystepcalculus.com, go to my site, buy my program if you want to pass calculus easy, or subscribe and see other videos I might make. And don’t forget about physics either. Thanks so much. Have a good one.