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On You & cAr If THE SpetdoM€ TER Te N ThE A STEADY 35 MPH Renvs Eithtr 0 Vecto e M TS AcleleraTiON PETDIcular T6 T+E VELOCTY or PE 02 FAlse Twue...

Question

On You & cAr If THE SpetdoM€ TER Te N ThE A STEADY 35 MPH Renvs Eithtr 0 Vecto e M TS AcleleraTiON PETDIcular T6 T+E VELOCTY or PE 02 FAlse Twue

on You & cAr If THE SpetdoM€ TER Te N ThE A STEADY 35 MPH Renvs Eithtr 0 Vecto e M TS AcleleraTiON PETDIcular T6 T+E VELOCTY or PE 02 FAlse Twue



Answers

An automobile travelling with a speed of $60 \mathrm{~km} / \mathrm{hr}$ can apply brakes to stop within a distance of $20 \mathrm{~m}$. If the car is going twice as fast, i.e., $120 \mathrm{~km} / \mathrm{h}$, the stopping distance will be (a) $20 \mathrm{~m}$ (b) $40 \mathrm{~m}$ (c) $60 \mathrm{~m}$ (d) $80 \mathrm{~m}$

All right question. 53 states that in your car you cover two meters during the 1st 1 second, four meters, getting the 2nd 1 second in 16 years during the 3rd 1 second and so forth was this motion a constant acceleration and explain. So here we know a pattern of increasing distance per second interval rates we serve start with two meters and then four meters and it's six years. And since the time frame above is constant and this is increasing, we do expect that this isn't an acceleration checkmark to that one. We want to see if it's constant acceleration. So does the situation presented here fit the cinematic egregious that we use for this section. Right? So what? We want to establish a pattern and then see if that pattern matches what we observe in our kid Max. Great. So for the very first time, travel that distance travel, that's a big two times t right? How are really looking all three of these? As a further pattern, I can establish that there's another pattern. President, Is that the distance at any time point? I'm saying we can look at this one. Here is two times the time interval So once two times one is two seconds plus the distance traveled in the interval before her race. That's two times t plus what we have here. So I mean, they sensed that the D three should be six meters. And then from there with Miss Dalgleish, What d t minus one minute equal. Okay, Yeah. Um, the team included two times the time interval minus one, plus the interest, the business traveler, the interval beforehand. So here, with this pattern, we can establish what this may look like. So you could say that created a map positions as a function of this. Um, with this pattern, you have to for the 1st 2nd 4 for the 2nd 2nd 6 for the 3rd 2nd etcetera. Class by expanding is out. I mean, as many as you want with the final term being two times T and so we can see that this this is an expansion. Think again, because this is too t here. We have a second t there and ever growing this pattern can be represented. A serious essentially right. Two times. T t plus one plus 1/2. You can explain that don't get tea plus T Square, so we're left with just rewriting it appear in a cup. This position is a function of time to be t plus T Square, where he could know for my kid Mannix. We have a simple equation for this. We have to be not tea plus 1/2 1 half a T squared. If we look at the difference opportunities to I'm so there's not much we can state that based on your own. Our velocity equals one meter per second. The celebration In order to have one in this term, Arcelor's passed me 2.0 meters per second squared. So based on this new, these are the two primaries and get a team. We do know that acceleration doesn't match your can vet the equations indicating that a is constant, as the question did pose. Hey,

So this question asked us to determine whether or not theme ocean in question is constant acceleration. Eso were given about the were given the distance that they cover in the 1st, 2nd, 2nd, 2nd and in the 3rd 2nd. Um so if we make a emotion diagram of this so it becomes quite clear what we're what we're trying Thio se or China work out. So we have They told that in the 1st 2nd they move 2 m Um se Mrs Timmy is after one second and then they told in the 2nd 2nd they move 4 m double that eso then after two seconds eso they live 4 m in the 2nd 2nd after two seconds and moved six seconds. Andre never told in the third in the third second they travel 6 m sees these Airil one second implements increments Uh, we can see that each time each time is we gave from as we go from each second the that we add, we add to eso each each each second we're adding 2 m to the journey. Uh, thio the distance that they traveled in that second, um so therefore that is the acceleration so if we If we stay down here, um, they acceleration off this eso It starts from rest service. Stephen Flynn the 1st 2nd, they're moving at 2 m per second. Mhm. Oh, well, they have traveled, uh, 2 m per second over the over the is one second on. Then we can see on here if we do another hour. Change of velocity is again 2 m per second. Yeah, on Then we can see on the 3rd 2nd again. So we have difference between four and six, which is also too. So Delta v here is also equals A to me it's per second on This says that this carries on, um indefinitely. So in other words, this is This is a constant acceleration where the acceleration is equal. Thio 2 m per second. Every second s. Oh, yes. This is our constant acceleration are off 2 m per second squared

All right. Question 2 51 states that using your velocity equation from the previous exercise find the corresponding distance equation assuming initial distances. Zero meters. How far do you travel while you accelerated your car and there's a him today is a convert units, but we'll get to that a second. We'll get that idea, but anyway, so this is our velocity function. We get, um, is actually from the integral in the equation in question to 49. So by taking the interval of that acceleration equation, we get equation for velocity. So that's where this comes from. I'd recommend doing from 2 49 or 2 58 just to find it if this doesn't make sense. But this question assumes you start there so we'll start from here. So if the velocity is the interval of the acceleration equation, then by that logic that the position of the equation is just the integral of our I'm glossy equation. So we'll continue this trend so we'll take the interval of this velocity creation from zero to T. He's going to be able to find the function for position, and then, after a certain time, we might find out where our position is. Some weaken a plug in our equation here 0.70 T. Cubed over three. If you're wondering why I left it in this format. Excuse me, I am is performed integral to the equation to 49. And that was a result. I didn't simplify its. That's why you may be thinking. Why would you not just write 1.44? Like what? The equivalent of that is divided by two. But it's all the same to me, so hopefully it's all the same to you. So we're doing the interval of this equation. Actually, really, it's It will be we're gonna do in terms of bounds or me. Indifferent, indefinite, integral because we weren't really told here what is told to look for the equation. So by doing that we have 0.70 came T to the foreign, this whole term now divided by 12 because of the three and the denominator. Previously, 1.44 t cubed over now six and finally 10.44 t squared or two and not found, plus C, but we're told. Also that's were initially at a distance of zero miles so that X T equals zero. We find that word initially at zero, this whole term equals zero plus c. So therefore C equals zero, and we don't need to consider it as, um doesn't offsets to our problem here so suddenly begin to solve for the X the position that Marantz at four after five seconds by substituting in five into our equation, and by doing that, we would find that we would have a position of any 1.1, too. And this is where the hint of you know, the question comes in. You'll need to convert time units because if you look at what we're given, this value will have units of miles per hour, times seconds, which is not particularly useful for anybody because you want position seconds over. Ours does not convert, So simply weaken. If we recognize in one hour there are 3600 seconds. Yeah. Then take a look at our sex. Our units, seconds cancels out hours, cancels out, and you're left with just miles, which would convert. Sorry, not convert would be calculated to be 0.0 2 to 5 miles. And I mean, the textbook mentions it feet. So if you convert that two feet, although it does it, this is a specify We know that in. Oh, sorry I'm doing this nominee will cancel out miles as a unit. So in one my own there are 5280 feet, which corresponds to a distance and feet of 119. So either of these answers are sufficient. Accurate. So whichever one you choose, use should be correct.

Question number couldn't be. The initial velocity is you Quito. Seven meter per second. The acceleration is a call to zero Point it me that parts again. This square This is what's two x elation? Time is equal. Do cool seconds. The planet roast is given by the prosecution of Motion. We call it you less it be solving this. We will get of Benin velocity as it 0.6 meet. Uh, but a sickening


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