solve-the-given-problems-the-vertical-displacement-y-in-mathrmcm-of-the-end-of-an-industrial-robot-3

Question

Solve the given problems.
The vertical displacement $y$ (in $\mathrm{cm}$ ) of the end of an industrial robot arm for each cycle is $y=2 t^{1.5}-	an 0.1 t,$ where $t$ is the time (in s). Find its vertical velocity for $t=15 \mathrm{s}$.

Carson Merrill · Accepted Answer

for this problem we have the vertical displacement at the end of an industrial robot arm. It&#x27;s going to be widely equals ju T. To the 1.5 mine ex candidate. 0.1 cheap. So when we evaluate this we know that we have different derivative rules that we know. So this the derivative of that would be Uh T to the 1.5 over the natural log of 1.5. And then the tangent of value when we take the derivative is going to be seeking squared of that value. And then because of the 0.1 inside we&#x27;d use chain rules. So we multiply the whole thing by 0.1. Um one way we can also evaluate this is by treating the function. Why as ffx and T as the value acts. I&#x27;m only here this we get F prime of X. Is this graph right here And we&#x27;re trying to evaluate it at 15 seconds. So we see the f prime of 15 is going to end up giving us a negative 8.4 and that cm per second.

Amy Jiang · Answer

I give it a B l t is equal to duty when it&#x27;s fortune over four post teeth word. Now our displacement is given by derivative of our velocity. So we just need to take the integral of our velocity. So integral over velocity is to tea when it&#x27;s fortune over four t squared beauty and this is this t squared minus 14 over to students, seven engines inverse of you ever, uh, for Batou, which is to but seeing as a solution Oh, actually, we&#x27;re also given in this, you know, information. We know that AT T is equal to zero s a secret video. So we have that if you call this Y zero is equal to zero minus seven and its interests of don&#x27;t This is also don&#x27;t see sooner that she is also because we have that y is equal to t squared minus seven tensions in verse of tea over to

Linh Vu · Answer

Thanks. Ju my last one tree Sorry goes day. And there was asked to find a 10 Pretty standard, actually equal to zero. So we need todo who&#x27;s, uh one way to do this Question is I will bring yes, my mystery Your country said to take right if I get that and entity by everything bythe step this way. We got the attention of the Kennedy 50 manager country as well. Wait, wait, wait until ready. You ready? And because I, uh I didn&#x27;t own the temptation to test and buy. Wait, I have a dream. Three. Until here. Is that him? The law?

Adam Deaton · Answer

you were given a function feta that represents the angular displacement as a pendulum moves in terms of tea, uh, units of time for us to find the maximum of dysfunction in the rate of change when t equals three. So to find the maximum, remember that our trick functions are always found it between minus one and one state absolute value lesson or equal to one in the 80 doesn&#x27;t change that. That just changed the period. It means that it&#x27;s gonna wiggle up and down faster, but not become larger is this implies that the the absolute value of theater for any time T is always listener ankle 2.2. That&#x27;s for any team, as is the statement over here about co sign system place that, um, they just found between minus 2.2. And, um, the last thing to confirm that the max, if ADA is actually point to, would be to check that, um, that data actually a teen&#x27;s Valium 0.2 for some tea if you choose T so that you&#x27;re getting consent of zero. So if you plug in t a zero for example, then we&#x27;ll get this value and we know it can be bigger than this value based on this inequality argument. So it does have a max of 0.2. Okay, So compute the rate of change. Um, all the rate of change means in like, a real world problem is that I have the derivative, so we just need to take the derivative of theta perspective T. So we&#x27;re gonna get eight times 80.2 times you mind. A sign of 18 two is, um, to ever tender one over five. So this is really 8/5 minus 8/5 times sign of 18. So the rate of change at this point in time, we just plug in t equals three, and we&#x27;ll get minus 8/5. Time sign, uh, eight times three, which is 24. This isn&#x27;t a nice number. Shaken thrown in your calculator if you want a new miracle answer. Um, but either way, this is our expression for the rate of change when t equals three

Gianna Calciano · Answer

and this problem we know completely. Revolution. It&#x27;s two minutes. That&#x27;s 360 degrees. So we need to set this up in a proportion with 1.5 minutes. Then we can do cross product multiplication. Doing this. We get X 3 to 70. Then we can take our 270 degrees and multiply by pi over 1 80 and we get three pi over two. These are two answers in degrees and radiance.

Zulfiqar Ali · Answer

Let&#x27;s write down the equation for instantaneous displacement. Our X t so displacement it a given time is equal to eight times. We&#x27;ll sign into omega T less fi. This is the equation for instantaneous displacement. Here is amplitude. Omega is and your frequency and find is the first difference. No, let&#x27;s to park. Okay, well, in the given case, X 08 Time T is equal to zero. Our displacement is given by ah, equal toe amplitude and equals 12 point five centimeter. And this implies Nate. If I must be equal to Muzito, so phase difference. Most vehicle to zero and X T is equal to eight times go sine omega t. We&#x27;ll also given the frequency F is equal to six point 68 hers. And we know that omega, which is an your frequent Sequels to buy yep and therefore to buy a physical to 42 ready in per second x&#x27;d displacement it through. Given time is equal to 12.5 Well, 12.5 is the amplitude 12.5 centimeter is the amplitude time school sign into 42. 42. Well, 42 is Omega Times T. So this is the uh, displacement? No, let&#x27;s draw away form. So the way form looks like this, right? No, this is on instant ing is displacement in the Y direction and in the X direction Nouri&#x27;s time. Now let&#x27;s to park be well, uh, if x t with displacement in the given time is equal to is equal to eight times go sign in tow Omega T plus Phi, right, We&#x27;ll make a d plus five. Then we lost is differential off displacement The X divided by d t equals minus a ah minus a time sign into omega de bliss fi multiply by omega So we get this by differentiating X with respect to time Well, no, it time he&#x27;s equal to zero but lost E equals the lost equals minus e dime Sign into fi times omega And this is the maximum. And this imply state by is equal to minus, uh, by divided by two. It&#x27;s minus by divided by two. This is minus pine the mighty, but to since ah signed minus by divided by two is equal to one signed minus by divided by two is equal to minus one, not one. So, uh, X&#x27;d is equal to a sine omega T is signed Omega T right. Eso displacement is equal to In which is 2.15 2.15 into Sign Omega, which is four point 63 4.63 times. Do you? Right? And the real form again looks like this.

Problem

Solve the given problems. The electric charge $q$…

Problem 51 Easy Difficulty

Solve the given problems.
The vertical displacement $y$ (in $\mathrm{cm}$ ) of the end of an industrial robot arm for each cycle is $y=2 t^{1.5}-\tan 0.1 t,$ where $t$ is the time (in s). Find its vertical velocity for $t=15 \mathrm{s}$.

Answer

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