the-position-of-a-ball-as-a-function-of-time-is-given-by-x50-mathrmm-mathrms-tleft-10-mathrmm-mathrm

Question

The position of a ball as a function of time is given by
$x=(5.0 \mathrm{m} / \mathrm{s}) t+\left(-10 \mathrm{m} / \mathrm{s}^{2}\right) t^{2} .$ (a) What are the initial position,
initial velocity, and acceleration of the ball? (b) Plot $x$ versus $t$ for
$t=0$ to $t=2.0 \mathrm{s}$ (c) Find the average velocity of the ball from
$t=0$ to $t=1.0 \mathrm{s}$ (d) Find the average speed of the ball between
$t=1.0 \mathrm{s}$ and $t=2.0 \mathrm{s} .$

Nathan Silvano · Accepted Answer

Okay, So in this problem, we have a function that describes the position of a particle. The function in his ex if course five D minus Stan T Square. Okay, so the first item of the problem, we need to discover the initial velocity, the initial position and the acceleration of this particle. Since this is ah, second degree function, we know that this should be accelerated movement. And we know that the generic immigration that describes, uh, position of a particle is x zero bolos V zero t plus a divided by two T square. Okay, so let&#x27;s look to the initial position. The initial position is when the time equals zero. So sporting T equals zero. We&#x27;re going simply have initial position off zero meters. And what about the initial velocity? The initial velocity? We can come there. That&#x27;s weird. In here we have X equals five key minus stand key square. So if we look here, we see that the zeroes needs to be five. So the initial velocity is just five meters for a second. What about the separation? Do the same thing. We just compare the genetic function we have to the position with the one we have in this particular problem. So Dan minus Stan needs to be close to a divided by two, which means that a is going to be minus trying t meters per second squared. This is the answer to the first item. The second item. We need to do a lot of dysfunction. Okay, let&#x27;s put a function here. We have Let&#x27;s see, ex grows five D minus Dan de square, and we need to blot the graph between the Times T CO zero and T Coast through. So thinks this is a second degree function. We know that the behavior of dysfunction of this graph should be a horrible and we just need to discover what is going to be the position and t because two seconds. Let&#x27;s find this. We have to position it&#x27;s gross five times, two miners 10 times for So this is just minus dirty minor starting in the position. Okay, so let&#x27;s see. So we need to remake his graph because we&#x27;re not gonna be able to a lot this graph in minus dirty with the X is like this. So let&#x27;s see, That&#x27;s pretty exes. Uh, here we know this is a second degree function and dysfunction has aken captivity negative because off the constant follows the teeth square. So we know that this function begins in zero. It grows up in two minus dirty. So we&#x27;re going to have a lot like this. This is the position the plot in T equals two seconds. In the third item, we need to discover the average velocity between the time deco zero anti equals one. So let&#x27;s see average. The last city is just the displacement divided by the difference in time difference. In time. We already have. It&#x27;s just one second and the displacement? Well, let&#x27;s see. We just need to discover what is the final position and t close one and the position Antico zero. We already know. So the position and t it goes one going to be five times one minus 10 times one. This is simply minus five. So the average velocity in this interval is just minus five minus. Mine is you know. So the answer to the third item is the average speed, the average velocity. I want to be minus five meters per second in the last item. We need to discover the average speed between worm into seconds. So let&#x27;s do the same thing again. We already know the position. Yeah, T equals one. But what is the position and the equals? Two seconds. So the position you&#x27;re going to be two. Sorry. Five times to minus 10 times four. So this is equal to 30 minus dirty meters. So the average velocity, it&#x27;s going to be attacks divided by daughter T. This is simply minor. Sturdy, minus minus five. Just going to come positive, divided by one. So this is just minus 25 meters per seconds. That&#x27;s different. Arrested to the problem. Thanks for watching.

Josh Broderick Phillips · Answer

So we&#x27;re given this equation of a bowl rolling down in a straight line and I&#x27;m just gonna be right. This is except T because it&#x27;s the same thing. It&#x27;s a function of time. And the first part is wondering what&#x27;s the position of the ball of various times? So for ex of one second, we&#x27;re gonna plug in for tea. So two stays the same, 3.6 multiplied by one, uh, plus 1.1 times what squared. And this is gonna equal, uh, negative 0.5 meters, uh, and then next part again, just plug in two seconds. So we have 2.0, you 0.6 plug in to, and this comes out to be 0.8 meters and then plug in three seconds. Class one point on three squared and this unequal 1.1 meters. Now, for the second part, we wanted the average velocity over this interval from one second, 23 seconds, three seconds. And this Delta V, what I&#x27;m gonna call is Delta X over Delta T. And so this is gonna equal Delta X will we want Exit three, which is 1.1 meter minus one minus 0.5 meters and then we&#x27;ll divide by the time interval. Three seconds minus one second on this comes out to be 10.8 meters per second. For the last part, we want to know that instantaneous velocity a two seconds of three seconds and so I can get this velocity function from the position function by taking the derivative. So, uh, Viv T it&#x27;s gonna equal d x t beachy. Ah. And so the constant was away and we&#x27;d have minus 3.6. Plus, uh, 1.1 times two is 2.2 p. And then to find the to plug it in again, So plug in two seconds and this equals 0.8 meters per second and three seconds, uh, equal, and we&#x27;ll plug in three. This equals three meters per second.

Nathan Silvano · Answer

Okay, so and this problem, we have a function. I described the position of a car as a function of time. That&#x27;s what we have. 50 plus minus five, actually, is not bliss. Miners five Chief minus 10 T square. Okay, so the problem wants to discover in the first item the initial position. D&#x27;oh! Initial velocity in the acceleration of the car. Okay, So since this is a second degree functions, it describes the movement of a car. We can come there with the generic away function. Describes the position of a particle which are at zero plus the zero T plus a divided by two T square. So if we compare is two equations we know this is the initial position. So the initial positions should be 50 road Initial position is 50 meters. The initial velocity is right here. The initial velocity isn&#x27;t here, So the initial velocity is minus five meters per second and the acceleration isn&#x27;t here. We can come. Everything&#x27;s one. So it&#x27;s simply just a divided by two. It goes, my understand. So the acceleration, it&#x27;s just miners. 20 meters per second square. Okay, this is the first. I tend of the problem in the second item we need to blocked and Graf off this movement from times T equals 02 times t equals true. So first of all, let&#x27;s discover the final position off the let&#x27;s discover the final position of the car in the instant T equals two. So we have acts of gross 15 minus five, T minus 10. He&#x27;s square. So when did time equals two seconds? This is going to be Let&#x27;s see, 50 minus 10 minus 40. This is just zero. So the Times chief was two seconds. The position of the car is zero meters. Okay, now we know this. We can plot the graph. Let&#x27;s see, we have time excess. Here. We have the position access reaching here. Just position access. This is the time access. So one time equals two seconds. Position off the car isn&#x27;t zero meters, and when time equals zero seconds, the position of the car using 50 meters. So since this is a second degree function, the behavior is a horrible. So it&#x27;s going to be a horrible like this one. So this is the graph off the movement of the car between the Times t equals zero antique owes to the third item. We need to discover what was the distance cover by the car in the 1st 2nd of the movement. Okay, so to discover the distance covered by the car, we just need to calculate the final position of the car when time, of course, one. So we&#x27;re going to have 15 minus five. I understand. So this is just 35 meters. So if you want to displacement of the car, how much they can travel, we just need to You just need to calculate. Let&#x27;s see. Displacement should be the final position, minus the initial position. So this is e close to minus 15 meter. So the answer to the third item I didn&#x27;t see, but that&#x27;s the answer to the ight and see is just displacement. Who&#x27;s minus 15 meters. Finally, the last item. We need to calculate the average velocity of the car between the first in the second second. Okay, let&#x27;s see. Average velocity is just displacement. Divided by time. We know the position in the 2nd 2 Mine is the position in the 2nd 1 divided by one position. Second to is, let&#x27;s see, uh, the position Seconds two is zero. Since we already calculated you. This is going to be zero miners. The position in 2nd 1 She&#x27;s 35 minus 35 divided by one. So the average velocity is just minus 35 meters per second. And that&#x27;s the final answer to the problem. Thanks for watching.

Suzanne W. · Answer

the position of a particle is given by R F T. Is equal to three T squared. I had minus seven. He scored. I had -7 T cubed J hat minus five T. To the negative two K. Hat. And units of meters. What is the velocity as a function of time? So a the velocity is the derivative. So six I had -42. J. had minus 30 T. to the -3. He had in the units of meters per second. Whoa. It took my apologies, drives one more time. So the velocity is the derivatives, there&#x27;s 60. I had minus 21 T squared J. Hat plus t. 10, tease the negative three. Okay hat in units of meters per second. Then the acceleration is equal to you. six I had -42 T. J. Hat -30 teams. The negative for Okay hat and units of meters per second squared part C. What is the particle&#x27;s velocity at tables? two seconds. So we add two seconds is equal to Well, I had -84 J. Hat 1st 1.25 he had in units of meters per second. What is the speed at equals one second in two equals three seconds. So for part the you&#x27;re finding the magnitude, So the magnitude of G at 1 2nd is equal to 24 m/s and three seconds Is equal to 190 years per second. Remember it? The square root of V X squared plus Y squared plus U C squared part E. What is the average velocity between two equals 1 and equals 2? So the average velocity equals R at 2- are at one over one second, Which is equal to nine. I had -49 J. Hat Plus 3.75 he had in units of meters per second.

Kevin Luu · Answer

Okay. Hello. So we&#x27;re gonna be looking at this function for acceleration. Uh, a of T is equal to 20 divided by t plus two squared. You know that at time zero, we have 20 at time. Zero, we have 10 times zero velocity is 20 and position is 10. So we&#x27;re gonna start by doing it for this one. So to find the, uh, anti derivative of a of T to find the velocity function var velocity, what we&#x27;re gonna do is we&#x27;re gonna take this and we are going to subtract one, because this is the same as tune 20 times 10 plus two to the power of Negative too. Which is the same, uh, which if we degrade it, it becomes 20 10 plus to to the car of negative one on. This is negative because this we&#x27;re dividing it by negative one, which then becomes 20 divided by 10 plus two plus c. And then we can solve for C. We know this is equal to 20 because that velocity, if we make this equal to zero, so we make t is equal to zero. So we get 10 20 plus two plus C equals 20 uh, So we get 20. No, this is negative. Sorry. So we get negative 10. So we get C is equal to 30. So our velocity is negative. 20 divided by T plus two plus 30 to find the position. We&#x27;re gonna integrate this again. So 30 is easy. 30 becomes 30 t. This is a bit trickier. So because t plus two is in the denominator, it&#x27;s gonna have a natural log. So we get the natural log of T plus two 20 stays the same. This is still negative and all that stuff plus C. Now we know that c r adds a T equals zero. The position is equal to 10 which is then equal to 30 times zero plus negative 20 times the natural log both T r zero plus two close. See, this cancels out the natural log of and then we get C minus 20 times natural log to it was 10. So C is equal to 10 plus 20 of the natural love, too, which, if you want an exam or exact value, is approximately 23.9. So if we put that in, we get s of t equals, uh, negative 20 in the natural love. Um T plus two last 30 t plus approximately 23.9 on the velocity once again is this

Amy Jiang · Answer

Okay, so report A We want to know when our ball starts the ground. So that&#x27;s wonderful. And function s entity is equal to go so we can factor out a 16 t from our turn here. Do we get 16 t times a negative T plus 96/16 6 So this is equal to zero. Okay, so we get to solutions when negative t plus six is equal to go and when 16 t is you could video. So this gives us when t is you could to six on when t is equal to zero. Okay. And I&#x27;ll for part B, we went to find or average speed of our ball from TZ federal to Tuz too. So that&#x27;s our change And why over our change. So that&#x27;s gonna be s evaluated. Cuts to minus s evaluated a thorough over a two minus Errol. So this gives us well as evaluated at two. That&#x27;s a negative 16 times to three part two plus 96 times too. So let&#x27;s put that into our calculator, and I get 128 and then we have us evaluated at so So that&#x27;s going to be Joe So we get 128 minus 0/2. So 128 divided by two is going to be equal to 64. And now we want to find our instantaneous rate of change. So that&#x27;s going to be or derivative. So that&#x27;s us prime at sea. That&#x27;s equal to our limits as T approaches some value. See, So we get, um, our function, which is negative 16 t Square plus 96 t And then we&#x27;re going to subject that by, um, our function evaluated at sea. So that&#x27;s going to be minus so plus a 16 c squared minus a 96 c all over t minus sea yet. So for party, we want to find all right derivative 20 is equal to two. So it&#x27;s plug that into our equation. So that&#x27;s going to be equal to the limits as t approaches to of negative 16 teach squared plus 96 t And then we have, um, play in our Steve for you said that 16 times two to the power of to minus 96 times too. So we have mice 128 over t minus to so Let&#x27;s fact there are numerator. Okay, so we can practice into a Let&#x27;s write that down here. The limits as t approaches to of negative 16 times are come T minus four and or a T minus two. So we see that we can cancel out that t minus still and now, using drugs up, we have negative 16 times two minus four. So that&#x27;s going to be an eight of 16 times native to which is equal to 32.

Problem

A cheetah can accelerate from rest to 25.0 $\math…

Problem 45 Hard Difficulty

Answer

(a) The Answer is $[\mathrm{zero}],[5 \mathrm{m} / \mathrm{s}]$ And $\left[-20 \mathrm{m} / \mathrm{s}^{2}\right]$
(b) SEE SOLUTION
(c) $-5 \mathrm{m} / \mathrm{s}$
(d) 25 $\mathrm{m} / \mathrm{s}$

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(a) The Answer is $[\mathrm{zero}],[5 \mathrm{m} / \mathrm{s}]$ And $\left[-20 \mathrm{m} / \mathrm{s}^{2}\right]$(b) SEE SOLUTION(c) $-5 \mathrm{m} / \mathrm{s}$(d) 25 $\mathrm{m} / \mathrm{s}$

Physics

Elyse G.

Christina K.

Liev B.

Marshall S.

Math Review - Intro

Algebra - Example 1

James S. WalkerPhysics

Elyse G.

Christina K.

Liev B.

Marshall S.

(a) The Answer is $[\mathrm{zero}],[5 \mathrm{m} / \mathrm{s}]$ And $\left[-20 \mathrm{m} / \mathrm{s}^{2}\right]$
(b) SEE SOLUTION
(c) $-5 \mathrm{m} / \mathrm{s}$
(d) 25 $\mathrm{m} / \mathrm{s}$

James S. Walker

Physics