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# Test help.

 Posts: 2,033 Add as FriendChallenge to a DebateSend a Message 9/16/2012 7:14:27 PMPosted: 4 years agoThis problem was on a test of my friend's, and she would like to know how to do it, someone to solve it, etc. because she's worried about her grade. I'm pretty poor/lazy at physics, so if someone could help, that'd be awesome.A car accelerates for 4 seconds, then maintains a constant velocity for 14 seconds. At the end of 18 seconds, it has traveled 1200 m.What is a) Its initial acceleration, andb) the distance at which it stopped accelerating?Now assume that the car decelerates at -12.5 m/s.How long does it take for it to come to a full stop, and at what distance?I miss the old members.
 Posts: 7,102 Add as FriendChallenge to a DebateSend a Message 9/16/2012 7:50:56 PMPosted: 4 years agoAt 9/16/2012 7:14:27 PM, Atheism wrote:This problem was on a test of my friend's, and she would like to know how to do it, someone to solve it, etc. because she's worried about her grade. I'm pretty poor/lazy at physics, so if someone could help, that'd be awesome.A car accelerates for 4 seconds, then maintains a constant velocity for 14 seconds. At the end of 18 seconds, it has traveled 1200 m.What is a) Its initial acceleration, andb) the distance at which it stopped accelerating?Now assume that the car decelerates at -12.5 m/s.How long does it take for it to come to a full stop, and at what distance?Welllllll, I have to be honest, I don't actually know the formula for this; I don't remember. So, at times like this, I'd try to figure it out logically. This is what I did.Let's first divide 1,200 by 18 to see what the speed would be if the car were moving at a constant velocity the entire time. We end up with 66.667.Now, we also know that one way or another, the car never reached 100 m/s. We know that, because it would have exceed 1,200 meters within those last 14 seconds alone. So, more than 66.667, and less than 100. Let's try 75.14 * 75 is 1,050.Now, let's add in the first four seconds of acceleration. If the highest speed reached is 75 m/s with 4 seconds to reach that velocity, then the acceleration would be 25 m/s.1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.The second question is much easier. At -12.5 m/s acceleration, you're looking at 1,200/12.5 = 96.So, it would take 96 seconds to decelerate to a full stop.The distance you'd travel is a little more tricky, though. Let's reduce the numbers down, so it's not as retarded. It would take 9.6 seconds to decelerate from 120 m/s to 0 at a rate of 12.5 m/s.1. 120 - 12.52. 107.5 - 12.53. 95 - 12.54. 82.5 - 12.55. 70 - 12.56. 57.5 - 12.57. 45 - 12.58. 32.5 - 12.59. 20 - 12.50.6. 7.5 - 7.5 (12.5 * 0.6 = 7.5) = 0120 + 107.5 + 95 + 82.5 + 70 + 57.5 + 45 + 32.5 + 20 + 7.5 = 637.5Scale that back up, and we're at 6,375 m.Lol, I know I'm not doing this the "official" way (there's undoubtedly algorithms and specific equations one should utilize), but this is still a viable way to, if nothing else, check your answers. :PI'm just too lazy to look it up right now; I honestly don't remember the official way to do it.
 Posts: 7,102 Add as FriendChallenge to a DebateSend a Message 9/16/2012 10:07:23 PMPosted: 4 years agoWell, coming back to this, I wonder why I started the first second at a stop... but, I guess it's best to always look over your answers to make sure you did them right.I initially stated:1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.Which is completely wrong... it would instead be:1 - 18.75 +2 - 37.5 +3 - 56.25 +4 - 75 =187.5 + (75 * 14) = 1237.5...which is wrong, so it couldn't be 75. I guess I was just figuring it in such a way that it would make sense.So, I think I'm going to try this on paper, instead, before I go looking for the acceleration transformation that applies to this (you're not left with much information).......well, the direction I ended up going was to reduce it to its smallest increment algebraically and work from there.What we have here is the initial acceleration applied four times in a stepwise fashion, then that acceleration four times over 14 times repeated... lol... which translates in math terms as:(x + 2x + 3x + 4x) + 14(4x) = 1,200.(10x) + 14(4x) = 1,20010x + 56x = 1,20066x = 1,200x = 1,200/66 = 18.181818218.1818182 * 4 = 72.7272728So, in those first four seconds, it was accelerating at 18.1818182 m/s, and it travelled 181.8181819 m by the end of those first four seconds. It thus traveled 72.7272728 m/s thereafter to finally reach 1,200 m at the end of 18 s.Hilariously, it works out.
 Posts: 11,204 Add as FriendChallenge to a DebateSend a Message 9/16/2012 10:35:23 PMPosted: 4 years agoAt 9/16/2012 7:50:56 PM, Ren wrote:At 9/16/2012 7:14:27 PM, Atheism wrote:This problem was on a test of my friend's, and she would like to know how to do it, someone to solve it, etc. because she's worried about her grade. I'm pretty poor/lazy at physics, so if someone could help, that'd be awesome.A car accelerates for 4 seconds, then maintains a constant velocity for 14 seconds. At the end of 18 seconds, it has traveled 1200 m.What is a) Its initial acceleration, andb) the distance at which it stopped accelerating?Now assume that the car decelerates at -12.5 m/s.How long does it take for it to come to a full stop, and at what distance?Welllllll, I have to be honest, I don't actually know the formula for this; I don't remember. So, at times like this, I'd try to figure it out logically. This is what I did.Let's first divide 1,200 by 18 to see what the speed would be if the car were moving at a constant velocity the entire time. We end up with 66.667.Now, we also know that one way or another, the car never reached 100 m/s. We know that, because it would have exceed 1,200 meters within those last 14 seconds alone. So, more than 66.667, and less than 100. Let's try 75.14 * 75 is 1,050.Now, let's add in the first four seconds of acceleration. If the highest speed reached is 75 m/s with 4 seconds to reach that velocity, then the acceleration would be 25 m/s.1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.The second question is much easier. At -12.5 m/s acceleration, you're looking at 1,200/12.5 = 96.So, it would take 96 seconds to decelerate to a full stop.The distance you'd travel is a little more tricky, though. Let's reduce the numbers down, so it's not as retarded. It would take 9.6 seconds to decelerate from 120 m/s to 0 at a rate of 12.5 m/s.1. 120 - 12.52. 107.5 - 12.53. 95 - 12.54. 82.5 - 12.55. 70 - 12.56. 57.5 - 12.57. 45 - 12.58. 32.5 - 12.59. 20 - 12.50.6. 7.5 - 7.5 (12.5 * 0.6 = 7.5) = 0120 + 107.5 + 95 + 82.5 + 70 + 57.5 + 45 + 32.5 + 20 + 7.5 = 637.5Scale that back up, and we're at 6,375 m.Lol, I know I'm not doing this the "official" way (there's undoubtedly algorithms and specific equations one should utilize), but this is still a viable way to, if nothing else, check your answers. :PI'm just too lazy to look it up right now; I honestly don't remember the official way to do it.wrong answer is wrong.The actually equation your looking for is thisd = .5(A)*t^2 + (vo)*td = distance, Ao = acceleration, vo = initial velocityHowever it should be noted that the above equation assumes a constant acceleration. In the problem, in the first 4 seconds it has a constant acceleration, and in the next 14 seconds, it has a constant velocity.Sod1 = .5(A)(t1)^2 [One can ignore the initial velocity, since an initial velocity of 0 is assumed.t1 = time, d1 = distance]d2 = Vo(t2) [One can ignore the acceleration portion, since acceleartion is 0]So right now there are 4 unknowns, and only 2 equations (for every unknown you need one equation).A third equation is needed.d1 + d2 = 1200. We know that the sum of the two distances are 1200 meters from the problems.The forth equation is as follows:v0 = A*t1. Acceleration*time = velocity.So using some substitution one arrives at one giant equation:d1 + d2 = .5(A)(t1)^2 + Vo(t2) = 1200d1 + d2 = .5(A)(t1)^2 + A*t1*(t2) = 1200.5*A*4^2 + A*14*4 = 1200Using basic algebraA = acceleration = 18.75Also find vo, since this will be important for the final problemA*t1.= 18.75*4 = 75 m/sFor finding the distance is stops acceleration, just find d1d1 = .5(18.75)(4)^2 = 150.For deacceleration, its just the same equation, except both velocity and acceleration need to be taken into account.So.d = .5(A)*t^2 + (vo)*tv0 = 75d = .5*(-12.5)*t^2+(75)*6the velocity is zeo at the stopv = 0 = At + vov = 0 =-12.5*t + 75 m/st = 6 secondsd = .5*(-12.5)*5^2+75*4 = 225t = 6 seconds, d = 225 metersOpen borders debate: http://www.debate.org...
 Posts: 14,075 Add as FriendChallenge to a DebateSend a Message 9/16/2012 11:48:03 PMPosted: 4 years ago"...which is wrong, so it couldn't be 75. I guess I was just figuring it in such a way that it would make sense."I do that all the time.#UnbanTheMadman "Some will sell their dreams for small desires Or lose the race to rats Get caught in ticking traps And start to dream of somewhere To relax their restless flight Somewhere out of a memory of lighted streets on quiet nights..." ~ Rush
 Posts: 855 Add as FriendChallenge to a DebateSend a Message 9/17/2012 3:15:09 AMPosted: 4 years agoAt 9/16/2012 10:07:23 PM, Ren wrote:Well, coming back to this, I wonder why I started the first second at a stop... but, I guess it's best to always look over your answers to make sure you did them right.I initially stated:1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.Which is completely wrong... it would instead be:1 - 18.75 +2 - 37.5 +3 - 56.25 +4 - 75 =187.5 + (75 * 14) = 1237.5...which is wrong, so it couldn't be 75. I guess I was just figuring it in such a way that it would make sense.So, I think I'm going to try this on paper, instead, before I go looking for the acceleration transformation that applies to this (you're not left with much information).......well, the direction I ended up going was to reduce it to its smallest increment algebraically and work from there.What we have here is the initial acceleration applied four times in a stepwise fashion, then that acceleration four times over 14 times repeated... lol... which translates in math terms as:(x + 2x + 3x + 4x) + 14(4x) = 1,200.(10x) + 14(4x) = 1,20010x + 56x = 1,20066x = 1,200x = 1,200/66 = 18.181818218.1818182 * 4 = 72.7272728So, in those first four seconds, it was accelerating at 18.1818182 m/s, and it travelled 181.8181819 m by the end of those first four seconds. It thus traveled 72.7272728 m/s thereafter to finally reach 1,200 m at the end of 18 s.Hilariously, it works out.It would have been impressive - had you figured out the correct answer in this way!The Holy Quran 29:19-20 See they not how Allah originates creation, then repeats it: truly that is easy for Allah. Say: "Travel through the earth and see how Allah did originate creation; so will Allah produce a later creation: for Allah has power over all things.
 Posts: 7,102 Add as FriendChallenge to a DebateSend a Message 9/17/2012 7:25:25 PMPosted: 4 years agoAt 9/17/2012 3:15:09 AM, baggins wrote:At 9/16/2012 10:07:23 PM, Ren wrote:Well, coming back to this, I wonder why I started the first second at a stop... but, I guess it's best to always look over your answers to make sure you did them right.I initially stated:1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.Which is completely wrong... it would instead be:1 - 18.75 +2 - 37.5 +3 - 56.25 +4 - 75 =187.5 + (75 * 14) = 1237.5...which is wrong, so it couldn't be 75. I guess I was just figuring it in such a way that it would make sense.So, I think I'm going to try this on paper, instead, before I go looking for the acceleration transformation that applies to this (you're not left with much information).......well, the direction I ended up going was to reduce it to its smallest increment algebraically and work from there.What we have here is the initial acceleration applied four times in a stepwise fashion, then that acceleration four times over 14 times repeated... lol... which translates in math terms as:(x + 2x + 3x + 4x) + 14(4x) = 1,200.(10x) + 14(4x) = 1,20010x + 56x = 1,20066x = 1,200x = 1,200/66 = 18.181818218.1818182 * 4 = 72.7272728So, in those first four seconds, it was accelerating at 18.1818182 m/s, and it travelled 181.8181819 m by the end of those first four seconds. It thus traveled 72.7272728 m/s thereafter to finally reach 1,200 m at the end of 18 s.Hilariously, it works out.It would have been impressive - had you figured out the correct answer in this way!72.7272 * 14 = 1018.18 + 181.8 = 1199.98Close enough?Bah.I think it was close enough. I'll bet it's right, all decimals considered. ;)So, you can color yourself impressed, or not, over a 0.01 margin of error. I was thrilled nonetheless. ^_^
 Posts: 7,102 Add as FriendChallenge to a DebateSend a Message 9/17/2012 7:31:44 PMPosted: 4 years agoAt 9/16/2012 10:35:23 PM, darkkermit wrote:t = 6 seconds, d = 225 meters1 - 12.5 + 12.52 - 25 + 12.53 - 37.5 + 12.54 - 50 + 12.55 - 62.5 + 12.56 - 75=/=1,200;12.5 + 25 + 37.5 + 50 + 62.5 + 75 = 262.5=/=225Wrong answer is wrong?(btw, I'm pretty sure my answer to that part of the question was right. Care to show how it's not?)
 Posts: 11,204 Add as FriendChallenge to a DebateSend a Message 9/17/2012 10:37:11 PMPosted: 4 years agoAt 9/17/2012 7:31:44 PM, Ren wrote:At 9/16/2012 10:35:23 PM, darkkermit wrote:t = 6 seconds, d = 225 meters1 - 12.5 + 12.52 - 25 + 12.53 - 37.5 + 12.54 - 50 + 12.55 - 62.5 + 12.56 - 75=/=1,200;12.5 + 25 + 37.5 + 50 + 62.5 + 75 = 262.5=/=225Wrong answer is wrong?(btw, I'm pretty sure my answer to that part of the question was right. Care to show how it's not?)No, because your doing the method wrong.First of all, for the first part there's no reason why the velocity should equal the distance. The velocity should be zero once it comes to a complete stop. Which it does because the initial velocity is 75 m/s.Second off, the equation for finding distance isd = (1/2)A*t^2 + v*tWhat your doing is a riemann's sum. This will only get you an approximate, but not the exact.v = (A)*t + voThis is the equation your basing the above numbers on. So what your doing is:d = sum(f(v)*(delta t),0,6)delta t = 1 second for your calculations, and you've been doing it from 1 to 6 seconds. However there's room for error. Because at 1/2 a second it isn't going at 12.5 seconds. 1.5 seconds isn't going to go at 25 seconds and so forth.The equation:d = (1/2)A*t^2 + v*tis what you use which is actually just the integral of the following:v = (A)*t + voOpen borders debate: http://www.debate.org...
 Posts: 855 Add as FriendChallenge to a DebateSend a Message 9/17/2012 10:54:25 PMPosted: 4 years agoAt 9/16/2012 10:07:23 PM, Ren wrote:Well, coming back to this, I wonder why I started the first second at a stop... but, I guess it's best to always look over your answers to make sure you did them right.I initially stated:1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.Which is completely wrong... it would instead be:1 - 18.75 +2 - 37.5 +3 - 56.25 +4 - 75 =You were correct till here. However you messed up between displacement and acceleration at this point.Let me explain. Suppose I go from velocity of 50m/s to 80m/s in 3 seconds then:1. My acceleration is 10 m/s^2 as my velocity increases by 10m/s every second. My speed would be:0sec -> 50m/s1sec -> 60m/s2sec -> 70m/s3sec -> 80m/sThis is same as what you have done. However you need to notice that 10m/s^2 is acceleration (or the rate at which velocity is increasing).2. My average speed is (50+80)/2 = 65m/s. Thus my displacement in these 3 seconds is 65*3 = 195m. This is not sum of all velocities in between.187.5 + (75 * 14) = 1237.5Adding up velocities does not give you displacement. Use (0+75)/2 as average velocity and 4 sec as time. Turns out this was correct guess.The Holy Quran 29:19-20 See they not how Allah originates creation, then repeats it: truly that is easy for Allah. Say: "Travel through the earth and see how Allah did originate creation; so will Allah produce a later creation: for Allah has power over all things.
 Posts: 7,102 Add as FriendChallenge to a DebateSend a Message 9/18/2012 5:42:42 AMPosted: 4 years agoAt 9/17/2012 10:37:11 PM, darkkermit wrote:At 9/17/2012 7:31:44 PM, Ren wrote:At 9/16/2012 10:35:23 PM, darkkermit wrote:t = 6 seconds, d = 225 meters1 - 12.5 + 12.52 - 25 + 12.53 - 37.5 + 12.54 - 50 + 12.55 - 62.5 + 12.56 - 75=/=1,200;12.5 + 25 + 37.5 + 50 + 62.5 + 75 = 262.5=/=225Wrong answer is wrong?(btw, I'm pretty sure my answer to that part of the question was right. Care to show how it's not?)No, because your doing the method wrong.First of all, for the first part there's no reason why the velocity should equal the distance. The velocity should be zero once it comes to a complete stop. Which it does because the initial velocity is 75 m/s.Second off, the equation for finding distance isd = (1/2)A*t^2 + v*tWhat your doing is a riemann's sum. This will only get you an approximate, but not the exact.v = (A)*t + voThis is the equation your basing the above numbers on. So what your doing is:d = sum(f(v)*(delta t),0,6)delta t = 1 second for your calculations, and you've been doing it from 1 to 6 seconds. However there's room for error. Because at 1/2 a second it isn't going at 12.5 seconds. 1.5 seconds isn't going to go at 25 seconds and so forth.The equation:d = (1/2)A*t^2 + v*tis what you use which is actually just the integral of the following:v = (A)*t + voThanks! ^_^
 Posts: 7,102 Add as FriendChallenge to a DebateSend a Message 9/18/2012 5:47:14 AMPosted: 4 years agoAt 9/17/2012 10:54:25 PM, baggins wrote:At 9/16/2012 10:07:23 PM, Ren wrote:Well, coming back to this, I wonder why I started the first second at a stop... but, I guess it's best to always look over your answers to make sure you did them right.I initially stated:1 - 02 - 253 - 504 - 75= 150 + 1,050 = 1,200So, the answer to a) is 25 m/s, and the answer to b) is 150 m.Which is completely wrong... it would instead be:1 - 18.75 +2 - 37.5 +3 - 56.25 +4 - 75 =You were correct till here. However you messed up between displacement and acceleration at this point.Let me explain. Suppose I go from velocity of 50m/s to 80m/s in 3 seconds then:1. My acceleration is 10 m/s^2 as my velocity increases by 10m/s every second. My speed would be:0sec -> 50m/s1sec -> 60m/s2sec -> 70m/s3sec -> 80m/sThis is same as what you have done. However you need to notice that 10m/s^2 is acceleration (or the rate at which velocity is increasing).2. My average speed is (50+80)/2 = 65m/s. Thus my displacement in these 3 seconds is 65*3 = 195m. This is not sum of all velocities in between.187.5 + (75 * 14) = 1237.5Adding up velocities does not give you displacement. Use (0+75)/2 as average velocity and 4 sec as time. Turns out this was correct guess.Oh yeah, you're absolutely right! I can't believe I made that mistake. :PThanks! ^_^