1 00:00:02,029 --> 00:00:10,269 Hi guys, some of you have requested me to send you more exercise solved, because you are having problems to solve exercise 12 and 13. 2 00:00:10,929 --> 00:00:13,730 So we will start with number 12. 3 00:00:14,369 --> 00:00:22,230 The wording says, at a specific moment, the speed of a moving object is 45 km per hour. 4 00:00:22,390 --> 00:00:24,870 So we will start by writing the data. 5 00:00:24,870 --> 00:00:43,350 so this is exercise 12, page 125. The data we have is that the velocity at the end of a motion is 45 6 00:00:43,350 --> 00:00:51,429 kilometers per hour, ok? And then it says if you began studying the motion one minute earlier, so 7 00:00:51,429 --> 00:00:56,469 the time that we've been studying the motion is one minute, okay, we write it 8 00:00:56,469 --> 00:01:02,829 here in the data, and the acceleration, which is constant, is 20 centimeters per 9 00:01:02,829 --> 00:01:09,209 second squared, so we write the acceleration 20 centimeters per second 10 00:01:09,209 --> 00:01:20,140 squared. What is the initial speed? So the unknown is the initial speed, so v1, of 11 00:01:20,140 --> 00:01:28,269 of the interval studied. What will the value of the speed be after one minute or another minute? 12 00:01:28,269 --> 00:01:34,269 So that's the second part that we will solve after finishing this. 13 00:01:34,269 --> 00:01:43,769 So the first thing that we observe here is that we have different units, and none of them is an international system unit. 14 00:01:43,769 --> 00:01:51,269 So the first step would be to convert these units into international system units. 15 00:01:51,269 --> 00:02:10,330 So, we write a first conversion factor, we write kilometers in the denominator and meters in the numerator, a 1 and a 1000, and for hours, we write hours in the numerator and seconds in the denominator, and 3600, okay? 16 00:02:10,330 --> 00:02:20,430 So, if you calculate, well, now hours cancel with hours, and we can get rid of kilometers in this way, and we have meters per second. 17 00:02:21,750 --> 00:02:30,610 And if you do this operation in your calculator, you will get a result of 12.5 meters per second. 18 00:02:30,610 --> 00:02:40,419 ok then the delta time is in minutes and we should have it in seconds well one 19 00:02:40,419 --> 00:02:45,159 minute by the way is 60 seconds we don't need to use conversion factor for for 20 00:02:45,159 --> 00:02:50,159 that and then 20 centimeters per second square we need to convert that into 21 00:02:50,159 --> 00:02:54,840 meters per second square so we write centimeters in the denominator meters 22 00:02:54,840 --> 00:03:01,560 numerator 1 and 100 we get rid of the centimeters and finally we have 23 00:03:01,560 --> 00:03:11,460 0.2 meters per second squared, okay? So once we have all the data in the 24 00:03:11,460 --> 00:03:18,780 international system we will start by, I'm going to delete this part here, we will 25 00:03:18,780 --> 00:03:28,090 start by solving this. So we write a solution now. For that we need to know 26 00:03:28,090 --> 00:03:31,990 what is the equation we are going to use, okay? And we are going to use the 27 00:03:31,990 --> 00:03:39,189 equation of the acceleration the solution says that is the speed variation over the 28 00:03:39,189 --> 00:03:47,710 time taken okay so and and this speed variation is always the final speed 29 00:03:47,710 --> 00:03:53,169 minus the initial speed over the time taken so we know the acceleration we 30 00:03:53,169 --> 00:03:59,090 know the final speed and we know the time taken so yes we need to solve for 31 00:03:59,090 --> 00:04:05,629 v1 or isolate v1. So we write the acceleration 0.2 meters per second 32 00:04:05,629 --> 00:04:14,870 squared, that's just by substituting in this equation v2 is 12.5 meters per 33 00:04:14,870 --> 00:04:25,009 second minus v1 over 60 seconds. Okay the first thing we can do is to pass this 60 34 00:04:25,009 --> 00:04:35,449 seconds okay from this point to this multiplying so we will do that and now 35 00:04:35,449 --> 00:04:45,389 we have that 12.5 meters per second minus the initial speed equals 0.2 meters 36 00:04:45,389 --> 00:04:53,009 per second square times 60 seconds so we cancel this with the square and we 37 00:04:53,009 --> 00:05:04,829 finally have units units of speed and now we do 60 times 0.2 is 12 meters per 38 00:05:04,829 --> 00:05:12,870 second and now we can pass V1 to the right and 12 to the left so we will have 39 00:05:12,870 --> 00:05:22,230 finally 12.5 meters per second minus 12 meters per second and that gives an 40 00:05:22,230 --> 00:05:29,430 initial value of 0.5 meters per second for the initial speed so we write the 41 00:05:29,430 --> 00:05:38,269 result okay so that's the the end of the first part and now we have a second part 42 00:05:38,269 --> 00:05:45,990 in the second part the wording says that what will the value of the speed be 43 00:05:45,990 --> 00:05:51,449 after another minute so now we we could have V1 and V2 for the second 44 00:05:51,449 --> 00:05:55,610 but in the second part what we are going to do is use the v2 we have in the first part 45 00:05:56,490 --> 00:06:01,370 that it was 12.5 meters per second 46 00:06:03,529 --> 00:06:09,529 and we are going to calculate a final speed so we could call that v3 for example right 47 00:06:10,170 --> 00:06:20,410 that's the unknown so now the equation we are going to use a equals the variation speed so v3 48 00:06:20,410 --> 00:06:28,750 minus v2 over the time that it continues being one minute or 60 seconds in this 49 00:06:28,750 --> 00:06:32,290 case so we write 0.2 50 00:06:32,290 --> 00:06:35,290 gosh sorry for that 51 00:06:35,290 --> 00:06:51,230 0.2 meters per second square times 60 seconds which is again 12 as we did 52 00:06:51,230 --> 00:07:07,129 before and now is v3 minus v2 that is 12.5 meters per second and we get a value 53 00:07:07,129 --> 00:07:16,310 of 12 meters per second equals v3 minus 12.5 meters per second if we pass to 54 00:07:16,310 --> 00:07:28,129 these these to this side summing up we will get a result of 24.5 meters per 55 00:07:28,129 --> 00:07:36,290 second okay and that's all for the exercise 12 okay you have any doubt you 56 00:07:36,290 --> 00:07:45,350 can use the discussion forum or which is in Spanish for the dudas okay and then I 57 00:07:45,350 --> 00:07:56,389 I will answer your doubts, but if any of you want to answer doubts to other peers, you can do it, and this would be a way of continuing with our collaborative work. 58 00:07:56,769 --> 00:08:08,649 By the way, that would be part of your final mark, so if you contribute to solve any doubt, that would be positive for your grade. 59 00:08:08,649 --> 00:08:16,850 Okay, so thank you for your attention and later on I will upload other video for exercise 13. See you!