5

Let s(t) 8t8 60t2 96t be the equation of motion for a particle: Find . function for the velocity u(t)Where does the velocity equal zero? [Hint: factor out the GCF:]...

Question

Let s(t) 8t8 60t2 96t be the equation of motion for a particle: Find . function for the velocity u(t)Where does the velocity equal zero? [Hint: factor out the GCF:] andFind a function for the acceleration of the particle: a(t)Question Help:VideoSubmit Question

Let s(t) 8t8 60t2 96t be the equation of motion for a particle: Find . function for the velocity u(t) Where does the velocity equal zero? [Hint: factor out the GCF:] and Find a function for the acceleration of the particle: a(t) Question Help: Video Submit Question



Answers

Find the velocity and acceleration of a particle whose position function is $x(t)=\sin (2 t)+\cos (t)$

So this video were given the position The position is given by square root of two t I had hospital T j plus feet of the negative TK Hap al or ASA determine the velocities you. So the velocity is the first derivative of position. So we're just gonna take the derivative off off with respect. The derivative of square root of two to you with respected teas. Discriminative too. I have says where routed to I had plus the derivative of each of the team and respected is just getting the tea. So plus either the T J hat plus the derivative of either the negative t with respected to use negative to the negatives T. K. So this is our but lost it reality, right? All right, Now the speed is the magnitude of the velocities are gonna determine the magnitude of beat. So we take each i j K component off the velocity and square and then add them together and take this forward of that so it's square. So we're gonna dig the spirit of two squared must. Either the T squared was negative. Eat the negativity squared, add them together and take a swim. So That's just two plus either the duty plus e to the negative. So this negative ghost was worse. Sprayers. All right, now we're gonna add these together. Now, we're just gonna rearrange things so that we can get rid of this square rooms. We're gonna move this either the to t right to the front. And then two, we're gonna move it. Right. So we're gonna switch these two, and now to we can write it as two times to the tee, times e to the negative. Why? What's either the tee times either The negative? This is just either the t plus negative. Well, t plus negative t is zero. So just either zero or just so we just wrote. So either TV crimes, either. The negativity is just a convoluted right. Now, when we look at this, we realize that we can rewrite business each of the t plus e to the negative. T all that square now, why is that? Well, if you look right over here and we actually distribute, so we foil but here either the to t plus either the tee times into the negative G force, either the teeth as either the negativity plus e to the negative to t. And now if we combine like terms so this and this are equal. So if we add them together, we get each of the two t plus each of the tee times you know, the to t plus two times to the tee times e to the negative t bust into the negative tooty. So this is exactly what we had over two square. So they're equipped. All right. Now, those square in the spare room cancels or left with either the T plus two are great. So we found the speed. Now the acceleration even think of it as the first derivative of velocity or the second derivative of the position. So now if we take the derivative of square root of two with respect to t well, that's just a cause. And so it's derivative it zero respect. Now, if we take the derivative off each of the tea with respect to t will, that just stays. Now we think the derivative negative e to the negative t. With respect to you, that's just positive. So our acceleration is zero. I have us e to the T J hat plus into the negative T. K. Uh, and that is our excellent

Okay. This question wants us to find the velocity, acceleration and speed of a particle with this position function. So to find the velocity, we just need to take the derivative of the position function which doing this component wise Rx component derivative, is to t our white component derivative is co sign t minus. Then we have to do the product rule co sign T minus T sai Inti and then for 1/3 component, we get negative scientist e plus scientist e plus t CO sign t and then we can see some simplifications. So we see that V A T just simplifies to Because this cancels and this cancels so just simplifies to to t in our first component, T scientist Ian, are y component antico sign t in our Z component. So from here we confined our acceleration, which is the derivative of velocity And then again, going component list We see our derivative of our first term is too. Our second component is Sai Inti plus Co sign Sorry t co sign T and the derivative of our third term is co sign T minus t Sign t So now we have a velocity and acceleration. So now we can just find our speed, which is the magnitude of velocity is the square root of the sums of the squares of the components. And we can just plug these in so our X component for velocity is too t are y component for velocity is t scientist E and R Z component is Tico santi. So now it's just square all these can we get four t squared plus t squared sine squared, t plus t squared co sign squared to you, and you can pull a couple things out here. So first we can pull a t squared out to give us sine squared t plus co sign squared T Plus four. Or we can usurp a faggot and identity to get T squared Times one plus four or square roots of five T squared, which simplifies two t Route five as our magnitude So T Route five is our philosophy, and we found our acceleration and velocity earlier

So for this problem, we want to you find our velocity and acceleration functions of our particle. But before we do that, we can see that we have a trig identities identity here in our position function, um, our salary and identity, which, if we factor out to here, we get two times sine squared t plus co sign squared teeth. And we know that signs where t Plus co sounds great. Tea is just equal to one. So our position is always going to be at two times one, which is just too, so we can see here that this is a constant. So when we find our velocity, we know that we're taking the derivative of our position function. So we're just taking the derivative of a constant which is going to end up being zero and the same thing for our acceleration, which is the derivative of velocity. So again, the derivative of zero is just going to be zero. So our velocity and acceleration

I guess we have our up t. It's equal to B squared minus one comma t were asked to find in philosophy. But that's this derivative of Artie. So that's two t common one. Okay, acceleration is this through the derivative of our velocity? So that's just to combat zone and in speed is equal to the magnitude of our velocity, which is square roots. Both 40 squared plus one.


Similar Solved Questions

5 answers
3x-2 2) Find the inverse function f-1(x) for f(x) = 7x+5
3x-2 2) Find the inverse function f-1(x) for f(x) = 7x+5...
5 answers
A series LRC circuit consists ofa 100-Q resistor; 0.1O0-uF capacitor and a 2.00-mH inductor connected across 120-V rms ac voltage source operating at 1000 At what frequency will this circuit be in resonance?GJot4764aeHenl
A series LRC circuit consists ofa 100-Q resistor; 0.1O0-uF capacitor and a 2.00-mH inductor connected across 120-V rms ac voltage source operating at 1000 At what frequency will this circuit be in resonance? GJot 4764 ae Henl...
5 answers
Question 294 ptsFreezing is an example of a process for whichAG is negative at high temperatures but positive at low temperaturesAH and A S are positive:AH,AS and AG are negative at all temperaturesAH is positive and A S is negative:AH and AS are negative:
Question 29 4 pts Freezing is an example of a process for which AG is negative at high temperatures but positive at low temperatures AH and A S are positive: AH,AS and AG are negative at all temperatures AH is positive and A S is negative: AH and AS are negative:...
5 answers
0^ +*s Usc 4 focmula Rur_txans la hon Lexis t0 fad 25s3 fll t2 t43 t 23h_fllouiaq_uactian _LS peciecLic with Persod Za _ Ed 2iyz_ flel= 04&40 a4t22a
0^ +*s Usc 4 focmula Rur_txans la hon Lexis t0 fad 25s3 fll t2 t43 t 23 h_fllouiaq_uactian _LS peciecLic with Persod Za _ Ed 2iyz_ flel= 04&40 a4t22a...
5 answers
To appraximate the length ot marsh_ 5neyor waiks* 350 melers Your answer one decimal place:)point_point thenand walks 2Z0 meterspoint (see figure= Approximate the length AC of the marsh (RauadDam
To appraximate the length ot marsh_ 5neyor waiks* 350 melers Your answer one decimal place:) point_ point then and walks 2Z0 meters point (see figure= Approximate the length AC of the marsh (Rauad Dam...
5 answers
Let $A$ be a set and $B=mathbb{R} ackslash A$. Show that every boundary point of $A$ is also a boundary point of $B$.
Let $A$ be a set and $B=mathbb{R} ackslash A$. Show that every boundary point of $A$ is also a boundary point of $B$....
1 answers
Use Warshalls algorithm to determine the Boolean reachability matrix R What should R be when vou finish? Do this first
Use Warshalls algorithm to determine the Boolean reachability matrix R What should R be when vou finish? Do this first...
5 answers
The resting metabolic cost bicycling for example. could be the cost associated with sitting still on the bicycle: further modification is work efficiency_ which is defined as: ertemal mechanical work work efficiency (6.10) metabolic ns ZcroWark metanolc cost
The resting metabolic cost bicycling for example. could be the cost associated with sitting still on the bicycle: further modification is work efficiency_ which is defined as: ertemal mechanical work work efficiency (6.10) metabolic ns ZcroWark metanolc cost...
1 answers
Suppose that a plot of the values of $\mathrm{M} 2$ and nominal GDP for a given country over 40 years shows that these two variables are very closely related. In particular, a plot of their ratio (nominal GDP/M2) yields very stable and easy-to-predict values. On the basis of this evidence, would you recommend the monetary authorities of this country to conduct monetary policy by focusing mostly on the money supply rather than on setting interest rates? Explain why.
Suppose that a plot of the values of $\mathrm{M} 2$ and nominal GDP for a given country over 40 years shows that these two variables are very closely related. In particular, a plot of their ratio (nominal GDP/M2) yields very stable and easy-to-predict values. On the basis of this evidence, would you...
4 answers
What are two examples of renewable energy sources?
What are two examples of renewable energy sources?...
5 answers
Across between 2 species of sunflowers with fertilization occurring but the embryos die before reaching maturity is which type of barrier?Hybrid breakdownKvbrid sterilityHybrid inviabilityQuestion 132 ptsThe first step for allopatric speciation to occur ischange in allele frequenciesgeographical isolation_adaptive radiation;
Across between 2 species of sunflowers with fertilization occurring but the embryos die before reaching maturity is which type of barrier? Hybrid breakdown Kvbrid sterility Hybrid inviability Question 13 2 pts The first step for allopatric speciation to occur is change in allele frequencies geograph...
5 answers
The maan height of five students 67,4 inches. If one of the students leaves, the mean height becomes 67 inches. What is the height of tha student that leaves?70 inches 69 inches65 inches 0 D. 72 inches
The maan height of five students 67,4 inches. If one of the students leaves, the mean height becomes 67 inches. What is the height of tha student that leaves? 70 inches 69 inches 65 inches 0 D. 72 inches...
5 answers
Which of the following is the triple integral for the function f(€,y,2) = (22 +y? + 22)3 bounded by a sphere with radius 2 centered at the origin written in spherical coordinates? Select the correct answer below:f f J p sin(p) dp dvp d02T 2T f J J p8 sin(w) dp dw d02T f J J p6 sin(v) dp dw d02T f f} 08 sin? (p) dp dp d0
Which of the following is the triple integral for the function f(€,y,2) = (22 +y? + 22)3 bounded by a sphere with radius 2 centered at the origin written in spherical coordinates? Select the correct answer below: f f J p sin(p) dp dvp d0 2T 2T f J J p8 sin(w) dp dw d0 2T f J J p6 sin(v) dp dw ...
5 answers
1- Which of the following molecules is a target of cAMP?PI3KPKBPKCPKA2- Which of the following molecules will no longer be a part ofthe plasma membrane?Group of answer choicesIP3PIP3DAGPI(4,5)P2
1- Which of the following molecules is a target of cAMP? PI3K PKB PKC PKA 2- Which of the following molecules will no longer be a part of the plasma membrane? Group of answer choices IP3 PIP3 DAG PI(4,5)P2...
4 answers
(10 points) Find the last three digits of 7220011
(10 points) Find the last three digits of 7220011...
5 answers
What is the amino acid A that is involved in the following reaction?4 + 2 CH;COCICH;COOCH,CH(COOH)NHCOCH; 2HCI
What is the amino acid A that is involved in the following reaction? 4 + 2 CH;COCI CH;COOCH,CH(COOH)NHCOCH; 2HCI...

-- 0.019554--