referring-to-example-2-17-suppose-the-speeder-red-car-is-traveling-with-a-constant-speed-of-25-mathr

Question

Referring to Example $2-17$ Suppose the speeder (red car) is traveling with a constant speed of $25 \mathrm{m} / \mathrm{s},$ and the maximum acceleration of the police car (blue car) is 3.8 $\mathrm{m} / \mathrm{s}^{2}$ . If the police car is to start from rest and catch the speeder in 15 s or less, what is the maximum head-start distance the speeder can have? Measure time from the moment the police car starts.

Nathan Silvano · Accepted Answer

Okay, so and this problem we have of bullies car, there was stuff, which means with initial velocity zero, we have, uh, another car I speeder with constant velocity off 25 meters per second. What else do you have? We know that the acceleration, the maximum acceleration off the police car is 3.8 meters for second square. We want to know what is the maximum distance this Peter can have from the police car. So the bullet scar is stocked chasing this Peter and catch this pewter under a time off 15 seconds. Okay, so let&#x27;s go. This Peter object A and the police car object be. We have our equation to describe the moment when the police car catches the this. Peter, we know that this moment, the final position off this Peter is equal the final position off the police car. So we just need to describe the position of this Peter in the position of the police car. The position of dispute er is going to be x eight equals x zero. A less v t axel away is what we want to discover. Because is the distance the maximum distance of this Peter from the police car in the beginning of the movement. Let&#x27;s see, What is the creation from for the police car? It&#x27;s going to be x zero b waas V zero t loss a d squared divided by two. So we just need two years This information that the final position of the both ours is the same. Then we&#x27;re going to have X, you know, a less 25 times 15 eco&#x27;s initial position. Come back here in the show position off. Ah, well, this car is zero, so initial position is going to be zero initial velocity of the police car is also zero. So this is going to be just three point eight times 15 square divided by true. So the maximum distance off the speeder. So the bullet scar King catcher catcher is going to be, let&#x27;s see three 0.8 times, 15 scrag divided by two minus 15 times 25. So the answer to this it the answer is just maximum had start. It&#x27;s going to be 52 point five meters. So this is the answer

Nathan Silvano · Answer

Okay, so in this problem, we have a speeder. Let&#x27;s call it an object. Hey, and we have a police car. Let&#x27;s call object. Be. And the problem says this Peter has a constant velocity off 15 meters per second and the police car starts from rest, which means with initial velocity off zero meters per second, the problem wants us to find out what must be the acceleration off the police car. So the king hey, can catch this, Peter after seven seconds. Okay. So what means physically catch this. Peter means that the final position off the speeder going to be equal the fire position off the police car. So since we know this, we just need to use We just need to discover equation that describes. That was the final position of this Peter and my equation that describes the fighter position off the police car. So let&#x27;s see. We know that the speeder has a cost and speed, so his position as a function of time, it&#x27;s going to be X. You&#x27;re away blows VT. I&#x27;m calling exit away, because is the initial position off this Peter and the position of the police car? It&#x27;s just going to be X zero b was the zero t plus 80 square divided by two because he has accelerated movements and, well, how do we solve this? We just need to use this equation here. We just need to match the two equations. They create the position off the speaker of the position of the police car. So this is just going to be x zero. A pull us VT equals x zero b pull us v zero t plus a T squared, divided by two. The initial position off the car and this Peter are this thing. So we just can consider this. And the velocity of it is Peter 15 times savin reaches the time and this is going to be called zero. There is the initial velocity off the police car, plus the acceleration. We want to discover times seven squared, divided by two. So let&#x27;s see the acceleration just going to be 105 times two divided bore divided for 49. So this is something around four point. What do you mean? Your final answer is going to be four point 28 meters per second square. This is the acceleration of the police car. Thanks for watching

Manish Kumar ( Iit K ) · Answer

Since the police card is speeding up with the lesson of two points 44m/s. Spy. Right? So we need to find that. And and uh and speed passes the 30 minutes with the Blues Car. So it&#x27;s Peter. This passes With the speed of 30 m per second time. So it have a constant velocity. So basically able to find out how much time passes before the speaker is overtaken by the police car. So we know that it is starting from this point. So if this this car is traveling semantic sense in kittens, so they then it should also travel at the same time. So that means 30 into t equals two X. Is called beautiful as happy to spend over here. This is excellent and zero for the Spider Man. And this new simplicity here. So you people half of the expenses, half of 2.44 entities but won T. And one ticket cancelled from here and discomfort to be 1.2. So he comes out with her t upon 1.2. So that&#x27;s willing to now divide party They had by 1.2. So it comes out to be see that comes out to be 24 point 5/9 right in the next scenario. What we need to find is that why how far uh by how far uh they have, how far does this peter get before the overtaken by police can&#x27;t. So we know that that distance that will do nothing but being to be so he is 30 into time. He is 30 Into time. TT 30 upon 1.2. So this will be 900 mm Divided by 1.2. So the distance will be 7377073 7.70. Uh Okay, thank you.

Surjit Tewari · Answer

question Martin too. The initial velocity is you equals zero. The positive X elation is a one equals 1.5 Me Dad, What a second is Squad. The time off acceleration is the one equal toe fives against the second acceleration is a two equal do minus two me that what is that going to swell that time or breaking is equality three seconds. Now using the plastic question or motion, we will find the final velocity. After the accelerating pace, the final velocity off perfects alerting face Everyone is the choir toe zero less a one the one This is equal to 1.5. Indo by is equal to 7.5 me that. But second no! The final velocity after the breaking is equal to veto equal to initial velocity V one Bless it. Do be do Substituting The values we do is equal to 7.5 minus No Indarti. This is a Quito one born fight made up but a second so that finally lost key is equal to 1.5 meters per second. No, that distance traveled during the acceleration pastry. That one is equality. Uh, it won. The one is Squire This is a quote, uh, in the 1.5 in five. It&#x27;s quiet. Three. Dublin is equal to 18.75 Meet us that distance traveled during the baking place. They do? Is it Cueto B one? They do less, Uh, air. Do the Dewey Square substituting the values he got. Two is equal to 7.5 in tow. Okay, Last, uh, into my nest to in tow. Nine. This will give us the traitor who is equal toe 13 point fight makers. Now the total distance traveled is equal to 18.75 Last 13.5. This is 1/4 of the total distance started to point 25 makers. This is the required answer.

Surjit Tewari · Answer

Could someone be it? The distance covered during the first X elation is is the one using second question of motion. The one is equal to initial lost zero less How you won even is quiet. Stop shooting the values. The one is uh Indo a one. A one has a value of 1.5. The one is by so we will get even. It didn&#x27;t want 75 Meet that this is the value of B one. No, let us find the velocity. Exhilaration one better The acceleration. One place has ended. So this we lost Please everyone equal toe initial lost zero less a one people one is 115 The one is five so even is equal to 7.5 meter. But second, the whole journey can be divided into two parts Here a one is the acceleration and the area to his ex elation. He had lost his 31 their veto And your velocity is zero. So that distance colored during this way, says Deven. And distance over during this place is a little. Now let us find that this tends Tito, they do is equal to initial lost, which is here everyone we want to minus uh So is it plus half a to do you do? It&#x27;s why substituting the values We were only 7.5 He who is three minus, huh? In the 2.1 in two days. What, so doing this? We will get the value of the two. 13 point Zito five made that. So the total bay stands Kevin from initial point, This capital equal to the one less they go, this is equal to 18.75 less. I didn y in Seattle fight. So total distance traveled list even pointed make us. And the velocity after the second phase is Mito B one less a new. This is equal to 7.5 minus 2.1 into a This is equal to 1.2 Meet that What is that good

Josh Broderick Phillips · Answer

and this problem, we have a car that&#x27;s starting a 25 meters per second. So I will call that our initial velocity V zero. Okay. And it&#x27;s ending at rest. So I know our final velocity is gonna be zero and takes a distance of 85 meters, which I&#x27;m gonna called Delta X in this case because that&#x27;s just the total distance has changed. So we have these three variables and we&#x27;re looking for acceleration. So we want to use this equation v squared. It&#x27;s vey initial squared, plus two a Delta X in this case and that we can just plug in. Zero squared is 25 squared, let&#x27;s to a 85 meters and so then 170 am Just gonna sell for a was negative 6 25 So a equals negative 3.7 meters per second squared

Problem

Referring to Example $2-17$ The speeder passes th…

Problem 112 Hard Difficulty

Answer

$52.5 \mathrm{~m}$

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