WEBVTT
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This is College Physics Answers
with Shaun Dychko
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We begin this question in the usual way
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by writing down the information
that we're given.
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We're told that the
light rail commuter train
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accelerates at 1.35
meters per second squared.
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It has a final top speed
of 80 kilometers per hour
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and it's going to come to rest...
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or sorry. It starts at rest, I should say.
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And our job is to figure out how long does
it take for it to reach this top speed
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given that it starts at rest.
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Now, when we're writing down the data,
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that's a good time to take care
of any unit conversion issues.
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Most of our formulas require MKS units
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that stands for meters,
kilograms and seconds.
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And you should convert all of
your information you're given
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into these 3 -
meters, kilograms and seconds.
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So, in this case, we have kilometers,
which is not good. We want meters.
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And we have hours, which is not good.
We want seconds.
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So, we multiply it by
1 hour for every 3600 seconds.
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And you could have multiplied by
1 hour for every 60 minutes
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and then times by 1 minute
for every 60 seconds.
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I just happen to have it memorized that
there are this many seconds in an hour.
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Then, times by 1000 meters per kilometer,
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and so the kilometers cancel
and the hours cancel,
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leaving us with meters over seconds.
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And this is 22.22 meters per second.
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So, the formula we start with is that the
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final speed is the initial speed
plus acceleration times time.
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And then, we'll subtract
initial speed from both sides
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and also switch the sides around,
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so that we have *at* on the left
and *v f* minus *v naught* on the right.
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And then, divide both sides by *a*.
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And we have time is final speed minus
initial speed divided by acceleration.
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So, that's 22.22 meters per second minus 0
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divided by 1.35 meters per second squared.
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And that gives 16.5 seconds.
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It is the time it takes for the train
to reach 80 kilometers per hour
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when it starts at rest.
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When the train is stopping,
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a typical stopping acceleration is
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negative 1.65 meters second squared.
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So, this is just the regular brakes
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as opposed to the emergency brakes
that he uses down here in part C.
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So, in part B, we are going
to reuse this formula for time.
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And, we have a final speed
of zero in this case.
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And then, initial speed is the
top speed of 22.22 meters per second
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and we divide that by a
negative 1.65 meters per second squared,
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giving us 13.5 seconds as a time
for the train to stop.
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And then, in an emergency, it can do
the stopping in 8.3 seconds if it has to.
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And our job is to figure out what
acceleration it would be experiencing,
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given this stopping
in this period of time.
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So, the top speed again
is 22.22 meters per second.
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So, 0 minus that, divided by 8.3 seconds
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and that gives negative
2.68 meters per second squared.
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It's the acceleration in an emergency.