WEBVTT 00:00:00.070 --> 00:00:02.368 This is College Physics Answers with Shaun Dychko 00:00:02.923 --> 00:00:04.912 We begin this question in the usual way 00:00:04.913 --> 00:00:07.319 by writing down the information that we're given. 00:00:07.798 --> 00:00:10.314 We're told that the light rail commuter train 00:00:10.315 --> 00:00:12.956 accelerates at 1.35 meters per second squared. 00:00:13.528 --> 00:00:16.407 It has a final top speed of 80 kilometers per hour 00:00:16.500 --> 00:00:18.363 and it's going to come to rest... 00:00:18.533 --> 00:00:20.402 or sorry. It starts at rest, I should say. 00:00:21.091 --> 00:00:25.427 And our job is to figure out how long does it take for it to reach this top speed 00:00:25.715 --> 00:00:26.895 given that it starts at rest. 00:00:27.570 --> 00:00:29.451 Now, when we're writing down the data, 00:00:29.452 --> 00:00:32.587 that's a good time to take care of any unit conversion issues. 00:00:33.052 --> 00:00:35.981 Most of our formulas require MKS units 00:00:36.290 --> 00:00:38.769 that stands for meters, kilograms and seconds. 00:00:38.990 --> 00:00:41.519 And you should convert all of your information you're given 00:00:41.520 --> 00:00:44.061 into these 3 - meters, kilograms and seconds. 00:00:44.202 --> 00:00:47.267 So, in this case, we have kilometers, which is not good. We want meters. 00:00:47.644 --> 00:00:50.035 And we have hours, which is not good. We want seconds. 00:00:50.601 --> 00:00:54.227 So, we multiply it by 1 hour for every 3600 seconds. 00:00:55.300 --> 00:00:58.528 And you could have multiplied by 1 hour for every 60 minutes 00:00:58.795 --> 00:01:00.832 and then times by 1 minute for every 60 seconds. 00:01:00.833 --> 00:01:03.846 I just happen to have it memorized that there are this many seconds in an hour. 00:01:04.938 --> 00:01:07.675 Then, times by 1000 meters per kilometer, 00:01:07.676 --> 00:01:09.995 and so the kilometers cancel and the hours cancel, 00:01:09.996 --> 00:01:11.774 leaving us with meters over seconds. 00:01:12.046 --> 00:01:14.362 And this is 22.22 meters per second. 00:01:16.113 --> 00:01:18.116 So, the formula we start with is that the 00:01:18.117 --> 00:01:21.212 final speed is the initial speed plus acceleration times time. 00:01:21.518 --> 00:01:25.234 And then, we'll subtract initial speed from both sides 00:01:26.046 --> 00:01:28.254 and also switch the sides around, 00:01:28.613 --> 00:01:33.476 so that we have at on the left and v f minus v naught on the right. 00:01:34.224 --> 00:01:36.195 And then, divide both sides by a. 00:01:37.165 --> 00:01:41.998 And we have time is final speed minus initial speed divided by acceleration. 00:01:42.844 --> 00:01:45.908 So, that's 22.22 meters per second minus 0 00:01:45.909 --> 00:01:49.258 divided by 1.35 meters per second squared. 00:01:49.596 --> 00:01:51.518 And that gives 16.5 seconds. 00:01:51.647 --> 00:01:55.501 It is the time it takes for the train to reach 80 kilometers per hour 00:01:55.502 --> 00:01:56.998 when it starts at rest. 00:01:58.661 --> 00:02:00.191 When the train is stopping, 00:02:00.945 --> 00:02:03.917 a typical stopping acceleration is 00:02:04.806 --> 00:02:07.431 negative 1.65 meters second squared. 00:02:07.432 --> 00:02:09.117 So, this is just the regular brakes 00:02:09.924 --> 00:02:14.229 as opposed to the emergency brakes that he uses down here in part C. 00:02:14.666 --> 00:02:18.031 So, in part B, we are going to reuse this formula for time. 00:02:18.705 --> 00:02:22.995 And, we have a final speed of zero in this case. 00:02:23.430 --> 00:02:27.710 And then, initial speed is the top speed of 22.22 meters per second 00:02:27.711 --> 00:02:31.128 and we divide that by a negative 1.65 meters per second squared, 00:02:31.412 --> 00:02:34.861 giving us 13.5 seconds as a time for the train to stop. 00:02:36.326 --> 00:02:41.774 And then, in an emergency, it can do the stopping in 8.3 seconds if it has to. 00:02:41.962 --> 00:02:46.440 And our job is to figure out what acceleration it would be experiencing, 00:02:46.441 --> 00:02:49.704 given this stopping in this period of time. 00:02:51.188 --> 00:02:55.235 So, the top speed again is 22.22 meters per second. 00:02:55.236 --> 00:02:59.096 So, 0 minus that, divided by 8.3 seconds 00:02:59.388 --> 00:03:02.926 and that gives negative 2.68 meters per second squared. 00:03:03.259 --> 00:03:05.840 It's the acceleration in an emergency.