5

And x = 0 when t = determine the velocity; position, and total distance particle is defined by the relation J = _ 3 mlsec Ifv = 6 mlsec The acceleration of a given ...

Question

And x = 0 when t = determine the velocity; position, and total distance particle is defined by the relation J = _ 3 mlsec Ifv = 6 mlsec The acceleration of a given traveled when t = 8 seconds_

and x = 0 when t = determine the velocity; position, and total distance particle is defined by the relation J = _ 3 mlsec Ifv = 6 mlsec The acceleration of a given traveled when t = 8 seconds_



Answers

The motion of a particle is defined by the relation $x=6 t^{4}-2 t^{3}-12 t^{2}+$ $3 t+3,$ where $x$ and $t$ are expressed in meters and seconds, respectively. Determine the time, the position, and the velocity when $a=0 .$

We're told that the motion of a particle is fine by the relationship. Exit goes 60 to the fourth minus two cubed minus 12 T squared plus three t plus three. What accent here expressed in meters and seconds. Determine the time, the position and velocity when the acceleration is zero. That's the first weekend. Take derivatives to get our velocity and celebration from our position. And then we can figure out the time when, um, our acceleration is zero and we get that that's happened that when t equals 2/3 of a second and we can plug that back in to our position and our velocity and we get the position is 0.26 meters and the velocity is minus 8.56 meters per second and obviously the acceleration at that 0.0

So in this problem were given a equation of motion. And we want to find the time, the position and the velocity when the acceleration is equal to zero. So we have Yeah, this formula for the equation of motion. Yeah. And we're going to go ahead and take the time derivative So d d t of the position, she'll give us the velocity. Yeah, yeah, yeah. So that would be 24 t cute. Minus 60 squared. I'm just 2040 plus three. And then if we take TV of duty of the velocity will give us the acceleration. 72 t squared and it's 12 t minus 24. So we want to know when the acceleration is zero so we can set that equal to zero and factor things out to simplify it. So that would give us 12 times 60 Square Dynasty Managed to is the zero. Yeah, and we see that this is a quadratic equations. We can go ahead and solve that, which gives us two solutions. So to use to third seconds. And thi is one half seconds, but we can go ahead and reject that one. We're going to stick with this one. Yeah. 0.667 seconds. And here you just want to go with the one that's the most physical. So at T equals two third seconds. We're just gonna plug that into our original formula for X. So plugging that into our first equation of motion Well, give us a position of 0.259 m. And now we want to plug two into our equation for velocity. So we'll call this one two, three. So now that we have this by plugging it into equation one, we're going to put this into equation, too. We'll get that. The velocity at this time is negative. Key point 56 m per second. And from above, we know that the time was 0.667 seconds. When the acceleration is ego

Seen this problem were given a you relation that defines the emotion of a particle. And we want to determine the time, the position and the velocity when the acceleration is zero. So we're giving that X is equal to 60 to the fourth minus two t cubed minus 12 t squared plus 32 plus three mhm. So the first thing that we want to do is take the derivative with respect. Um, dx DT so we can find the lawsuit. So during that would give us mhm and then to find the acceleration we take the derivative of that should give us Yeah. So when a is equal to zero Yeah. So I need your t squared minus 12. T 24 is equal to zero, so and we can go ahead and factor this so it's easier to solve. So, b 12 times, sixties squared minus T minus two is equal to zero. Then we can, uh, see that there's two solutions using the quadratic formula. That would be t is two thirds No, and to use one half of a second. But we're going to go ahead and reject that one and go with this solution So at this time, we're just going to plug that in to our first equation. That's what we started with. So plugging this for T until equation one consulting give us a exposition of 0.259 leaders. Then we're also going to plug this into our equation for velocity. We'll call it equation, too. Okay, which will give us a velocity at that time negative 8.56 m per second. And all that negative sign tells us that they are going in the opposite direction as we've defined our access.

Well given lead. The lost T factor is equal to pre high camp less six minus to t into J cab On the unities. Meet up our second position. It some moment is given by integral o d r. The limits are from zero to R, which is a cool too integral off we DT and the limits of Integral are from zero to t and from here, position back to her heart. Physical to integral. Most limits are from zero to t into three by cab less six finalists to t. Jacob, right and therefore ah, unit director R and D D as well here. So the unit factor are Is it going to three d I camp less. Six D minus. T Square J cap. No position. Let's find a position into these equal to one supposition it is equal to one is three cap. Let's six minus one J cab, which is equal to three. I cap miss five. Jacob lists five. Jake right and also position eight e o. T. Is equal to pray is given by R is equal to nine. Ali Cat Bless 18 minus line 18 minus line. G camp, which is equal to nine. I can't less. Nine j cap on position. And now a displacement is equal to the difference of these two. So your prints in position is equal to nine. I camp list nine J cap minus tricky. I can this five a cab, and this difference is equal to six icapp less forge a cab, major.


Similar Solved Questions

5 answers
11 1 2014 Jaao Udao 1 1 Josonure 1
1 1 1 2014 Jaao Udao 1 1 Josonure 1...
5 answers
The rate constant k for a certain reaction is measured at two different temperatures:temperature 71.0 "C 1.9 x 10556.0 *C36Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy Ea for this reaction_Round your answer to 2 'significant digits_mol2
The rate constant k for a certain reaction is measured at two different temperatures: temperature 71.0 "C 1.9 x 105 56.0 *C 36 Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy Ea for this reaction_ Round your answer to 2 'significant digits_ mol 2...
5 answers
I3 6 8 1 1 97 8 1 1 g 1 8 1 1 3 H L 6 8 1 3 J } 1 I W L 1 13 2 h F 1 84 6 1 0 { 1 5 8 1 3 3 J 3 1 1 3 i 1 H 8 | 1 Ye J Db # W ] { 22222222-3
I3 6 8 1 1 97 8 1 1 g 1 8 1 1 3 H L 6 8 1 3 J } 1 I W L 1 13 2 h F 1 84 6 1 0 { 1 5 8 1 3 3 J 3 1 1 3 i 1 H 8 | 1 Ye J Db # W ] { 22222222- 3...
5 answers
Letbe3 X 4 matrix with column vectorsVI; V2, V3, V4. Decide which of the following statements are true O false. Justify Your answers_The columns of A must be linearly dependent_The rows of must be linearly dependent.The matrix AAT is symmetric.(iii) The identity AAT = AT A holds (iv) If Ax = 0, then the vector x is perpendicular to all the three row vectors of AThe equation Ax = b has a solution if and only if b € span{V1, V2, V3, V4}_
Let be 3 X 4 matrix with column vectors VI; V2, V3, V4. Decide which of the following statements are true O false. Justify Your answers_ The columns of A must be linearly dependent_ The rows of must be linearly dependent. The matrix AAT is symmetric. (iii) The identity AAT = AT A holds (iv) If Ax = ...
1 answers
Cunular Bandwagon Non MnrnnA SuItL Io} ngument Wtelling He1s VW 1 L Inhomosnrudls Vny pulite T man F either iX Suzvuu truth 1 date. SuPpOr Ihc police or L L 1 nnuor nurts L told Mulmn 1 MA notdc Wncne Ln
Cunular Bandwagon Non MnrnnA SuItL Io} ngument W telling He1s VW 1 L Inhomosnrudls Vny pulite T man F either iX Suzvuu truth 1 date. SuPpOr Ihc police or L L 1 nnuor nurts L told Mulmn 1 MA notdc Wncne Ln...
4 answers
(10 points) Sketch the graph of a function that satisfies all the conditions below: =f'() = f'(7) = 0, f(0) = 3 <0 if , < lor 5 < I < 7, > 0 if 1 < "< 5 0r > 7, f" () < 0 il 2 < I < 6, (x) > 0 if ? < 2 0" T > 6
(10 points) Sketch the graph of a function that satisfies all the conditions below: =f'() = f'(7) = 0, f(0) = 3 <0 if , < lor 5 < I < 7, > 0 if 1 < "< 5 0r > 7, f" () < 0 il 2 < I < 6, (x) > 0 if ? < 2 0" T > 6...
1 answers
A venturi meter, shown in Fig. P3.128, is a carefully designed constriction whose pressure difference is a measure of the flow rate in a pipe. Using Bernoulli's equation for steady incompressible flow with no losses, show that the flow rate $Q$ is related to the manometer reading $h$ by $$Q=\frac{A_{2}}{\sqrt{1-\left(D_{2} / D_{1}\right)^{4}}} \sqrt{\frac{2 g h\left(\rho_{M}-\rho\right)}{\rho}}$$ where $\rho_{M}$ is the density of the manometer fluid.
A venturi meter, shown in Fig. P3.128, is a carefully designed constriction whose pressure difference is a measure of the flow rate in a pipe. Using Bernoulli's equation for steady incompressible flow with no losses, show that the flow rate $Q$ is related to the manometer reading $h$ by $$Q=\fr...
5 answers
Solve the dlifference equationT(t) ~(t -I) = 421
Solve the dlifference equation T(t) ~(t -I) = 421...
1 answers
Use the table of integrals in this section to find or evaluate each integral. $$\int \frac{3 x^{2}}{2+4 x} d x$$
Use the table of integrals in this section to find or evaluate each integral. $$\int \frac{3 x^{2}}{2+4 x} d x$$...
1 answers
In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of $25.0 \mathrm{cm} / \mathrm{s}$ in traveling $50.0 \mathrm{cm}$ from the starting point, what was the angle of inclination of the track? Draw a graph of $v_{x}(t)$ when the positive $x$ -axis points down the track.
In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of $25.0 \mathrm{cm} / \mathrm{s}$ in traveling $50.0 \mathrm{cm}$ from the starting point, what was the angle of inclination of the track? Draw a graph of $v_...
5 answers
74 Me erad volves the rmalnlng trigonomctlc lunctions Dor$ cos 0 >sausfylng the glven conditions. (Il an answer unoclnedUndeneos
74 Me erad volves the rmalnlng trigonomctlc lunctions Dor$ cos 0 > sausfylng the glven conditions. (Il an answer unoclned Undeneos...
5 answers
QUESTION 3Collision theory predicts all of the following EXCEPT thatA reaction will not occur if the collision occurs with energy that is less than the activation energy:Frequency of collisions will increase with increasing temperature.A reaction will only occur if the collision geometry is correctMore successful collisions will occur for reaction with larger activation energy:
QUESTION 3 Collision theory predicts all of the following EXCEPT that A reaction will not occur if the collision occurs with energy that is less than the activation energy: Frequency of collisions will increase with increasing temperature. A reaction will only occur if the collision geometry is corr...
5 answers
6.4 Second-order linear ODEs with constant coefficientsFind the general solution of the following second order DEs with constant coefficients: d2y dy d2y dy +2 3y = ( + 9y = 0 dx d2 dx;
6.4 Second-order linear ODEs with constant coefficients Find the general solution of the following second order DEs with constant coefficients: d2y dy d2y dy +2 3y = ( + 9y = 0 dx d2 dx;...
5 answers
0 fi all valesP for-kichZnmay Lonve %e5 a{?
0 fi all vales P for-kich Znmay Lonve %e5 a{?...

-- 0.019268--