Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?

Video transcript

Welcome back, everyone. We are making observations about a blender and here's, here's what I'm going to do here. I'm actually going to set up a graph for our motions of our blender over time. I'm gonna make our X axis time and I'm going to make our Y axis revolutions per minute. And here is the order in which the activities of this blender occur. First, we are told that the blender starts from rest at a time of zero and then at a time of two seconds, it reaches a point of 18,500 revolutions per minute. Now, we are then told that it maintains this speed for eight seconds. So that means eight plus two is 10 right there and then it is going to come to a complete stop in a time of 2.5 seconds making 10 plus 2. 12.5. Here. Now, we are tasked with finding what is the total number of revolutions made. Let's go over our answer. Choices. Here we have a is 3160 revolutions, B 1.9 times 10 to the fifth revolutions C revolutions or D 6320 revolutions. All right. So what do we do here? Well, the reason I set up this graph is in order to determine the total number of evolutions, we can just find the area of this trapezoid that I have created here in order to find the total number of revolutions over the entire time interval. So here's how we are going to do this. We know that the entirety the the entire length of this base is 12.5 seconds and the entire length of the top here is eight seconds. Now the formula for the area of a trapezoid as a reminder is one half times the let's say top plus the base times the height. Now we are almost ready to plug in all of our values except we need to make sure that our revolutions per minute are in revolutions per second. So let's convert that real quick. We have 18,500 revolutions per one minute and we know in one minute there is 60 seconds. So these units are going to cancel out. This gives us 308.33 revolutions per second. Great. So now we are ready to find the area of our trapezoid. So the area which just as a reminder is going to be our total number of revolutions here is equal to one half times the length of the top, which is eight times the length of the bottom, which is 12.5 times our height, which is three oh 8.33 revolutions per second. And you plug all of this in your calculator. We get a final answer of 3160 revolutions which corresponds to our final answer. Choice of a Thank you all so much for watching. I hope this video helped. We will see you all in the next one.