A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t) = 50.0 cm + (2.00 cm/s)t − (0.0625 cm/s2)t2. (b) At what time t is the velocity of the turtle zero?

Video transcript

Welcome back everybody. We are taking a look at a train which I will represent with this box right here. And this train is traveling to the right? Let me redo that here to the right along a straight railway of track. Now we are given the position of this train as a function of time and we are tasked with finding when at what time is the velocity of the train equal to zero? Well, we know that the derivative of position is going to be velocity. So if we take the derivative of this equation right here, we'll find velocity, then we can set that equal to zero and solve for time. So first, let's start out with our derivative here. So for taking the derivative, we're just going to take it term by term. Alright, so the derivative of this first term. Well, it's just a constant. So it will be zero plus derivative. The second term, the T. Is just going to disappear. So this will just be 3.15. And then the derivative of the last term. We're going to use the power rule here. So this too is going to come down in front. The exponent will now be one and we have minus two times 0.0, 3 - four times t. Great. Now, this of course we know is to be velocity. So let's set this entire thing equal to zero and then solve for T. We have that zero is equal to 3.15- times 0.03-4 times t. Now here's what I'm gonna do. I'm gonna add this term to both sides here. Right? So let's see. We have plus 0.3 to four T. And you'll see that on the right here. These terms are going to cancel out. So now we are left with 3.15 is equal to two times all of this times our T. Now to isolate our T. Value. We'll just go ahead and divide both sides by this term. Right here, all the numbers attached to the T. Let me go ahead and write this on the other side as well. You'll see that now this cancels out on this side, so now he has T. Is equal to all of this. So when you plug this into your calculator, you get that T. Is equal to 48.6 seconds, which corresponds to our answer choice of a Thank you all so much for watching. Hope this video helped. We will see you all in the next one.