You are watching: A light-rail commuter train accelerates

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This is university Physics Answers through Shaun Dychko We begin this inquiry in the usual method by writing down the info that we\"re given. We\"re told the the light rail commuter train increases at 1.35 meter per 2nd squared. It has actually a final top speed of 80 kilometers per hour and also it\"s walk to involved rest... Or sorry. The starts at rest, I must say. And our project is to figure out just how long does it take because that it to reach this height speed provided that that starts at rest. Now, once we\"re creating down the data, that\"s a good time come take treatment of any kind of unit conversion issues. Many of our formulas call for MKS systems that means meters, kilograms and seconds. And you should convert all of your information you\"re given into these 3 - meters, kilograms and also seconds. So, in this case, we have kilometers, i beg your pardon is not good. We want meters. And also we have actually hours, i beg your pardon is not good. We want seconds. So, we multiply the by 1 hour for every 3600 seconds. And you can have multiplied by 1 hour for every 60 minutes and also then time by 1 minute for every 60 seconds. I just occur to have actually it memorized the there are this numerous seconds in an hour. Then, times by 1000 meters every kilometer, and so the kilometers cancel and also the hrs cancel, leaving us v meters over seconds. And also this is 22.22 meters per second. So, the formula we begin with is that the final speed is the initial speed plus acceleration times time. And also then, we\"ll subtract initial rate from both political parties and additionally switch the sides around, so that we have actually at top top the left and v f minus v nothing on the right. And also then, division both sides by a. And also we have actually time is last speed minus early stage speed split by acceleration. So, that\"s 22.22 meters per second minus 0 separated by 1.35 meters per 2nd squared. And that offers 16.5 seconds. That is the moment it takes for the train to reach 80 kilometers every hour once it starts at rest. Once the train is stopping, a usual stopping acceleration is negative 1.65 meters second squared. So, this is just the continuous brakes as opposed to the emergency brakes that he offers down right here in component C. So, in part B, we room going come reuse this formula for time. And, we have a final speed of zero in this case. And then, initial speed is the height speed the 22.22 meter per second and we division that by a an unfavorable 1.65 meters per second squared, offering us 13.5 seconds as a time for the train to stop. And also then, in an emergency, it deserve to do the stopping in 8.3 secs if it has actually to. And also our job is to number out what acceleration it would certainly be experiencing, given this preventing in this duration of time. So, the top speed again is 22.22 meters every second. So, 0 minus that, separated by 8.3 seconds and also that gives negative 2.68 meters per 2nd squared. It\"s the acceleration in one emergency.

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