WEBVTT 00:00:00.070 --> 00:00:02.368 This is College Physics Answers with Shaun Dychko 00:00:03.042 --> 00:00:06.188 We begin this question by writing down the information we've been given. 00:00:06.717 --> 00:00:11.894 We know that the baseball stops in a period of 1.85 milliseconds 00:00:12.244 --> 00:00:14.996 and we'll convert this milliseconds into seconds 00:00:14.997 --> 00:00:18.723 because it's a nice... nice time at the beginning of a question 00:00:18.724 --> 00:00:22.384 when you're writing down data to take care of any unit conversion issues 00:00:22.690 --> 00:00:28.159 and we know that our formulas require meters, kilograms and seconds. 00:00:28.160 --> 00:00:30.257 We're always working in MKS units 00:00:30.689 --> 00:00:32.583 and so this is milliseconds, 00:00:32.849 --> 00:00:34.730 which means we have to change it into seconds. 00:00:35.238 --> 00:00:39.465 And milli is the metric prefix meaning times 10 to the minus 3. 00:00:39.711 --> 00:00:43.264 And so, we put a 'times 10 to the minus 3' 00:00:43.494 --> 00:00:46.103 in place of the milli prefix. 00:00:46.726 --> 00:00:49.428 And so, now, we have 1.85 times 10 to the minus 3 seconds. 00:00:51.429 --> 00:00:56.527 The deceleration is 2.1 times 00:00:56.528 --> 00:00:58.555 10 to the 4 meters per second squared. 00:00:58.747 --> 00:01:01.052 And I wrote a negative there because 00:01:01.461 --> 00:01:06.643 this deceleration is opposing the initially positive velocity, 00:01:06.988 --> 00:01:11.305 which is all kind of made up in a way. 00:01:11.306 --> 00:01:14.303 You can decide what your coordinate system is going to be. 00:01:14.661 --> 00:01:18.242 Let's assume that to the right is positive 00:01:18.527 --> 00:01:21.181 and that's... So, that's the direction of the initial velocity. 00:01:22.121 --> 00:01:26.918 And since we've made that coordinate system positive to the right 00:01:27.289 --> 00:01:30.708 and we know that the acceleration is opposing this initial velocity 00:01:30.709 --> 00:01:32.331 because it has continued to slow down. 00:01:32.426 --> 00:01:37.178 That means the acceleration is directed to the left and it is therefore a negative. 00:01:40.258 --> 00:01:43.511 Okay. And final velocity is 0 00:01:43.513 --> 00:01:46.384 because the ball comes to a stop in this bit. 00:01:47.697 --> 00:01:52.563 And we have this formula for final velocity equals v naught plus at 00:01:52.916 --> 00:01:58.345 and we'll subtract acceleration times time from both sides 00:01:59.377 --> 00:02:00.779 making it disappear from the right 00:02:01.234 --> 00:02:02.476 and having it appear on the left. 00:02:02.477 --> 00:02:05.040 So, v minus at equals v naught 00:02:05.540 --> 00:02:07.391 and we'll switch the sides around. 00:02:08.103 --> 00:02:09.900 And so, we have our initial velocity. 00:02:10.381 --> 00:02:13.971 It is the final velocity minus acceleration times time. 00:02:14.501 --> 00:02:16.095 And then, substituting in our numbers, 00:02:16.115 --> 00:02:20.844 we have 0 minus negative 2.1 times 10 to the 4 meters per second squared 00:02:21.427 --> 00:02:23.605 times 1.85 times 10 to the minus 3 seconds, 00:02:23.606 --> 00:02:27.380 giving us an answer of 38.9 meters per second, 00:02:27.382 --> 00:02:28.882 must have been the initial velocity, 00:02:29.186 --> 00:02:31.793 which is about 140 kilometers an hour.