In what other situations can you use the distance formula?
In what other situations can you use the distance formula?You don't even need to be watching a space race.As long as you know two pieces of information for the formula D=RT,you can calculate any moving vehicle or object.Now, the next time you're in a car,you can let your friends know exactly when you'll be arriving,how fast you're going,or the distance you'll travel.It's as simple as DIRT.
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it turns out he had the faster rocket
D=RT 240 miles equals x times 3 hours.Divide both sides by 3 hours.This will leave x isolated on the right side of the equation.240 miles divided by 3 hours is 80 miles over 1 hour.Bleebop's rate is 80 miles per hour.Wow, even though Bleebop got there one hour later,it turns out he had the faster rocket.Mark seems pretty upset,but with aliens, you can never really tell.Thanks to DIRT, you now know how to calculate distance,rate,and time.
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The only problem is that they are starting from different asteroids
Do you have a friend or a sibling that's always competing with you to see who's the fastest?Our alien friends Bleebop and Mark are having the same debate with their custom-built rockets,and they've asked us to be the judge of a space race to their moon.The only problem is that they are starting from different asteroids.Bleebop is on an asteroid 240 miles from the moon,and Mark is on one 150 miles away.Don't worry, it's not rocket science.Solving this equation is as simple as DIRT.We can decide who the winner isusing the D=RT formula, or DIRT.
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Still think Mark is faster?
Mark finished first,so start with his rocket.Remembering DIRT, write down D=RT.150 miles equals x times 2 hours.Divide both sides by 2 hours.This will leave x isolated on the right side of the equation.150 miles divided by 2 hours is 75 miles over 1 hour.Mark's rate is 75 miles per hour.That's what mph means.It's the amount of miles over one hour.Still think Mark is faster?Let's set up the same equation for Bleebop and see.
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let's check out the results with our DIRT equation
Looks like Mark has the faster rocket,but let's check out the results with our DIRT equation.Begin by setting up a chart.Make four columns and three rows.Use DIRT to remember what to fill in.Each rocket will have information for distance, rate, and time.Mark's rocket went 150 miles,we don't know the rate,and he got there in 2 hours.Bleebop's rocket went 240 miles,we don't know the rate,and the time is 1 hour after Mark,or 3 hours.Because we don't know Mark or Bleebop's rate,that number is going to be a variable in each equation,which we'll represent with x.We'll solve the equation for the variable to find its value.
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It'll be up to us to find the rate
This stands for distance equals rate times time.In the case of Bleebop and Mark,we will only know the distance they traveled and the time it took for them to get to the finish line.It'll be up to us to find the rate and who is faster.Let's turn to the race now and see what information we get.Three,two,one,blast off!Bleebop and Mark's rockets go zipping across the galaxy towards their moon,dodging clunky meteorites and loopy space buggies.After a few close calls with a wandering satellite,Mark arrives first in two hours,and Bleebop gets there one hour later.
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The duration of thinking can vary greatly for a variety of reasons
But the duration of a thought will vary significantly depending on its routes,pitstops, and destination.In this case, when you perceive a threatening stimulus,you'll invoke a fear startle response.Similar to the knee-jerk response,a startle can be involuntary and quite fast.If the string twangs loud enough,you might react in less than 65 milliseconds.More likely though, your startle reaction will be based on sight.Our eyes can process an image as quickly as 13 milliseconds,but computation of what you're seeing and determining the danger it poses can take as long as 180 to 200 milliseconds.In that time the arrow will have gained a head start of about 13 meters.The target is far enough away that you're got just enough of a chance to catch up,if you can quickly, and quite literally,think your way out.
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The rate of these thoughts varies according to myelination and axon diameter
Which means that given a sufficiently long, myelinated or large-diameter neuron,your thoughts actually could win the race.But there a wrinkle.The arrow and thought don leave the gate at the same time;first the arrow fires, then once you perceive it,your signal can start down its path.Processing images or music, participating in inner speech,and recalling memories all require complicated neural pathways that are nowhere close to the linearity of the knee-jerk reflex.The speed at which these thoughts occur is mostly consistent,with variations based on myelination and axon diameter.
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These compounded factors can raise the speed of an action potential as high
These compounded factors can raise the speed of an action potential as high as 432 kilometers per hour.There plenty of variation: some people think faster than others,and your own speed of thought changes throughout your lifetime.In particular, as you reach old age,the myelin sheath covering your axons wears down,and other neuronal structures degrade.Back to the dastardly experiment.Arrows shot from recurve bows fly,on average, around 240 kilometers per hour.
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speeds can be boosted with myelination and increased axon diameter
Speed is distance divided by time,so this signal travels somewhere between 120 to 240 kilometers per hour.The initial action potential accounts for 1 to 5 milliseconds and synaptic transmissions only take .1 to .5 milliseconds,so the bulk of that time is spent within the axons.This is consistent with research findings that the average individual neuron sends signals at around 180 kilometers per hour.But speeds can be boosted with myelination and increased axon diameter.Myelin is a fatty sheath that insulates an axon,preventing electrical currents from leaking out.Meanwhile, axons with larger diameters offer less internal resistance.
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We factor in the number of neurons involved and the distance the signal has to travel
We must also factor in the number of neurons involved and the distance the signal has to travel.Let see what this looks like in a simple pathway your knee-jerk reflex.A strike to your patellar tendon triggers an electrical impulse that travels up a sensory neuron to your spine.There the signal branches, and for the sake of simplicity,wel consider the segment that jumps into a motor neuron to journey back down your leg.The total length of the neurons in that pathway is about 1 meter in someone who is 5 foot 5 inches,and on average it takes 15 to 30 milliseconds from strike to kick.
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the key factors that determine how quickly you think
They transmit signals down their axons by way of electrical impulses,or action potentials.One neuron can then pass that signal to the next at a synapse by way of chemical neurotransmitters.The signal is received by the next neuron dendrites,propagated down its axon,and passed further along.So, the key factors that determine how quickly you think include how long it takes to generate an initial action potential;propagate it down the length of the axon;and transport it through the synapse.
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who wins that race?
Your mortal enemy has captured you and hooked you up to a bizarre experiment.He extended your nervous system with one very long neuron to a target about 70 meters away.At some point, he going to fire an arrow.If you can then think a thought to the target before the arrow hits it,hel let you go.So who wins that race?In order to answer, we have to examine the hardware of thought: neurons.The human brain has about 86 billion of these cells.
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We all have our own unique ladder.Be mindful of yours
Next time you notice yourself reacting to your experience,pay focused attention to your ladder.
Ask yourself what beliefs are at play,where do they come from?What data and observations did you filter in as a result of your beliefs,and why?Are your assumptions valid and supported by facts?Would a different set of assumptions create different feelings,and result in new and better conclusions and actions?We all have our own unique ladder.Be mindful of yours,and help others to see theirs.
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ur beliefs were short-circuited by the ladder of the other individual
What just happened here?What changed? Why is this so significant?In our parking lot example,our beliefs were short-circuited by the ladder of the other individual.My wife is in labor,I need to get there quick,there's a parking spot. Whew!Oh, jeez, I cut someone off.I'd better apologize quickly so they don't think I'm a jerk.But what if we were able to short-circuit our ladders ourselves?Proactively, by choice?Guess what? We can!Let's return to our unique human function of free will.
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finally our last rung
Next time someone tries to cut me off,tires will be smoking on the pavement as I squeal past them into my spot.And finally our last rung: we take action.We back up, pull up behind his car,honk our horn, and roll down our window to scream a few choice words as well.Now imagine,he walks over quickly, apologizing.His wife, who's almost due with their first baby,called him from inside the mall to say she is in labor and needs to get to the hospital immediately.We're momentarily shocked,apologize profusely,and wish him luck as he rushes toward the entrance.
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How did the fifth and sixth steps happen
That stupid jerk, didn't his parents teach him anything?How could he not see my signal light?He must never pay attention!Why does he think he's more important than anyone else?Jumping quickly to the fifth rung,we conclude that this guy is heartless, inconsiderate,he needs to be taught a lesson and put in his place.We feel angry, frustrated,vindictive, justified.On our sixth rung,we adjust our beliefs based on the experience.That's the last time I give in!
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How do the steps happen
Who cares that it's sunny out and the birds are chirping?The 50% off sign outside of your favorite store is meaningless.You filter in the sensation of your grip tightening on the wheel,you feel your blood pressure rise,you hear the squeal of your brakes,and you notice the expression on the face of the other driver as he pulls in front of you and quickly looks away.Time for our third rung.Ever since you were young,your parents taught you the importance of waiting in line and taking your turn.You live and die by the rule of first come, first served.And now this guy has just stolen your spot.What gives?Up to the fourth rung we go.Watch closely as our assumptions take over and our story creates itself.
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run it up the ladder to see how this all works
On the seventh and final rung,we take action based on our adjusted beliefs.Still with me? Great!Let's take a real-life example and run it up the ladder to see how this all works.Have you ever been cut off in a parking lot, signal light on as you steer toward your coveted spot,only to slam on your brakes at the last minute as someone pulls in front of you and steals your spot away?Imagine that experience and notice all of the data and observations landing on the first rung of your ladder.Now let's watch what we pay attention to on the second rung.
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The third to sixth steps
On to the third rung.We assign meaning to the information we have filtered through.This is where we start to interpret what our information is telling us.On our fourth rung,a very crucial thing happens.We develop assumptions based on the meaning we created on the previous rung,and we start to blur the distinction between what is fact and what is story.On the fifth rung,we develop conclusions based on our assumptions.This is also where our emotional reactions are created.On the sixth rung,we adjust our beliefs about the world around us,including the person or people involved in our experience of the moment.
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Let's focus on what happens on each rung of the ladder
This process happens thousands of times a day without us knowing it.Let's focus on what happens on each rung of the ladder.On the first rung, we have the raw data and observations of our experience.This is very similar to what someone watching a video recording of our experience would see.Moving up to the second rung,we filter in specific information and details from our experience.We unknowingly filter based on our preferences, tendencies,and many other aspects that we believe are important.
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The Ladder of Inference
Imagine a microscopic-sized ladder contained in the part of our brain that we'll label our subconscious.The Ladder of Inference,which was first proposed by Harvard professor Chris Argyris,is the basis of this model.Every time we interact with someone,that experience enters the ladder at the bottom.That same experience zips up the ladder in the blink of an eye,exiting at the top.
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