You are watching: A light-rail commuter train accelerates
This is college Physics Answers v Shaun Dychko We begin this inquiry in the usual means by writing down the information that we"re given. We"re told the the light rail commuter train increases at 1.35 meters per 2nd squared. It has a final top rate of 80 kilometers per hour and also it"s going to involved rest... Or sorry. It starts at rest, I have to say. And our job is to number out exactly how long does that take because that it to with this height speed offered that it starts at rest. Now, when we"re writing down the data, that"s a good time to take care of any unit conversion issues. Most of ours formulas require MKS devices that means meters, kilograms and seconds. And you need to convert every one of your info you"re offered into this 3 - meters, kilograms and seconds. So, in this case, we have actually kilometers, which is no good. We want meters. And also we have hours, i m sorry is no good. We desire seconds. So, we multiply it by 1 hour because that every 3600 seconds. And you could have multiply by 1 hour for every 60 minutes and then times by 1 minute for every 60 seconds. I just happen to have it memorized the there room this many seconds in an hour. Then, time by 1000 meters every kilometer, and so the kilometers cancel and also the hours cancel, leaving us through meters over seconds. And this is 22.22 meters per second. So, the formula we begin with is the the final speed is the initial speed plus acceleration time time. And then, we"ll subtract initial rate from both political parties and also switch the political parties around, so that we have at on the left and also v f minus v nothing on the right. And then, division both political parties by a. And also we have actually time is last speed minus early stage speed separated by acceleration. So, that"s 22.22 meters per second minus 0 split by 1.35 meters per second squared. And also that offers 16.5 seconds. That is the time it takes for the train to with 80 kilometers every hour when it starts at rest. Once the train is stopping, a usual stopping acceleration is an unfavorable 1.65 meters 2nd squared. So, this is just the constant brakes together opposed come the emergency brakes the he uses down here in component C. So, in part B, we space going come reuse this formula because that time. And, we have actually a final speed of zero in this case. And then, initial rate is the peak speed of 22.22 meters per 2nd and we division that through a an unfavorable 1.65 meters per second squared, offering us 13.5 secs as a time for the train to stop. And also then, in one emergency, it can do the stopping in 8.3 secs if it has to. And our task is to figure out what acceleration it would be experiencing, given this preventing in this duration of time. So, the optimal speed again is 22.22 meters every second. So, 0 minus that, split by 8.3 seconds and also that gives negative 2.68 meter per second squared. It"s the acceleration in an emergency.
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