(3) “Hamster Wheel”: Lots Of Speed… No Velocity

Do you ever feel like you are just “spinning your wheels”?   Like you are exerting a lot of energy, and there seems to be a lot of motion but not much movement or progress?

Or, maybe you can see movement happening, but you realize that you are a little off course.  How hard is it to change your direction, even just a little?  

Today we’ll talk about the fascinating relationship between movement over distance, speed, velocity and acceleration – and I’m talking about personal growth, not just physics.

For today’s post we will cover FOUR four terms:


SCIENTIFIC DEFINITION: “(noun) the act or process of moving, especially a change of position or posture” (from Merriam-Webster.com )

GEOFF’S DEFINITION: Getting to someplace new.  A new location on the earth, a new place in your thinking, a new position on a topic.


SCIENTIFIC DEFINITION: “a: the act or state of moving swiftly.  b: the magnitude of a velocity irrespective of direction” (from Merriam-Webster.com )

GEOFF’S DEFINITION: Measures how fast you went.


SCIENTIFIC DEFINITION:  “(noun) the quickness of motion (speed); the rate of change of position along a straight line (or in the same direction) with respect to time” (from Merriam-Webster.com )

GEOFF’S DEFINITION: Measures how fast you “got there” (“there” is someplace new – geographically, emotionally, intellectually)


SCIENTIFIC DEFINITION:  “the act or process of moving faster or happening more quickly; the rate of change of velocity with respect to time” (from Merriam-Webster.com )

GEOFF’S DEFINITION: Measures how much you (1) sped up, (2) slowed down or (3) changed direction while getting to your destination


THE PHYSICS:   I find the physics relationship of these four ideas very cool.  Each succeeding idea is just the previous idea divided by time.

Sir Isaac Newton’s Second Law of Motion states:

“The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.”

Let’s start with the Physical/Mathematical relationship among these concepts:

  • Movement requires that there be a difference in location from one moment in time to another.
    • The space between these locations is “distance”. How “far” the object moved.
  • Speed is how fast you are changing position from moment to moment, regardless of direction.
  • Velocity is the ratio of the change in position (BOTH distance and direction) over the time it took to change.
  • Acceleration is the ratio of the change in velocity (including direction) over the time it took to change.


So, “distance” is a pretty simple idea for most everyone.  Almost every moment of every day we are looking at things around us and without thinking about doing it, we are estimating their distance.  Is that other car too close for me to pull out?  If I cut the end off the banana how far do I need to move the knife so I don’t cut my hand?  How far do I need to jump to get over this puddle?  If you are pretty good at these kind of mindless estimates be thankful – not every one is.  (Some people have vision impairment issues that make their sense of depth-perception very poor, and their ability to accurately estimate distance is weak.)

d = p2 – p1

Distance = change in position


Speed is actually easier to estimate that you might think.  Since speed is simply the distance something moved divided by the time it took to move there. 

If you see a car coming toward you and when you see the car is one football field away (100 yards, or 300 feet) and it takes the car 6 seconds to reach you, then you know both distance and time.   300 feet / 6 seconds = 50 feet/second = 34 mph.  Technically, this is the “average speed”.  The car could have traveling much faster than 34 mph when it was 300 feet away, but then slowed down as it got closer to you.  So, it’s average speed over that period was 34 mph.

But with speed, we don’t need to identify the direction of the movement.  So a car that could go 150 feet forward and then 150 in reverse all in 6 seconds, still has a speed of 34 mph, but it ended up in the exact spot.


s = d / t

Speed  =  (change in position) / time to make the change




Velocity is basically speed with a direction.  So the velocity of the car we discussed above might be 34 mph north.


Just like speed was the “change in position” (or distance) divided by time, acceleration is the “change in speed” over the time it takes to make the change.

I made the point above that the 34 mph we calculated was really just the average speed.  If the car did change it’s speed OR it’s velocity (same speed, different direction) then there must have been some acceleration. 

So, if the car was going 20 mph when it was 300 feet away from you, then it was going 50 mph when it reached you means that it had an average speed of 34 mph.   That required an acceleration of (50 mph-20 mph) / 6 seconds = 5 mph/second/second.   In other words, each second it was going 5mph faster.   From 20 mph to 25 mph (1 second), to 30 mph (2 sec), to 35 mph (3 sec), to 40 mph (4 sec), to 45 mph (5 sec), to 50 mph (6 sec).



a = (v2 – v1) / t

Acceleration = change in velocity / time to make the change


    • Movement:          300 feet
    • Speed (average): 34 miles/hour
    • Velocity:        34 miles/hour northeast
    • Acceleration:   5 mph/second/second

NASA APPLICATION: How will it help humans get to Mars

Just thinking about all of the velocities and accelerations involved in getting to Mars is mind blowing.

Just a short list of the different ones is given to the right.  Each of them is significant in determining the proper timing of the launch and the duration of the flight.  Being off by even a little bit could mean disaster for a journey of this distance.  Go too fast (too much velocity) and you could arrive at the right spot in the galaxy but several days to early – Mars wouldn’t be there yet.  Taking off at the wrong time on Earth could mean that you start your trip on a path away from Mars and have to pull a galactic u-turn.

Once the rocket starts to lift off it’s velocity will increase from 0 mph to 1 mph, then faster and faster.  In order to leave Earth’s atmosphere it will need to reach “escape velocity” which is about 25,000 mph!!  Think of the amount of acceleration that will require.   But the rocket can only carry so much fuel.  So they must achieve that amount of acceleration in a very short amount of time.  All of that has to be figured out by NASA.  Exactly how much acceleration is needed?  How long will have to be maintained?  How much fuel that will require?   How much mass does that add to the rocket?  (Mass is covered in an earlier blog post)   This is exactly the kind of problem solving that leads to the expression that when something isn’t hard we say, “It’s not rocket science”.  

Even if you get all of the math right, you still have to worry about using the right measurement system.  Just ask NASA what happened to their Mars Climate Orbiter.   

You can read more about the story here, but in a nutshell…  one team designed the spacecraft and it’s onboard acceleration system using English units (inches/feet, pounds) and another team designed the program to send instructions to the orbiter using Metric units (meters, kilograms)

  • Velocity of the Earth’s rotation
  • Velocity of the Earth’s orbit around the sun
  • Velocity of Mars’s orbit around the sun
  • Escape Velocity  needed for the rocket to leave Earth’s atmosphere
  • Acceleration due to gravity
  • Acceleration of the rockets inside Earth’s gravity
  • Acceleration of the rockets in space

LIFE APPLICATION: How does it get YOU to your M.A.R.S.

Let’s apply today’s terms to our personal growth.  The first term is “movement”.  To determine movement, you must start by knowing “where” something is when you start measuring.

“Where” are you today?  

  • Where are you physically?
    • Which room of the house or office?
    • Which floor of a building?
    • Which part of town?
  • Where are you relationally?
    • With your spouse/boyfriend/girlfriend?
    • With your best friend?
    • With your boss/co-workers?
  • Where are you professionally?
    • Which career field are you in?
    • What level of responsibility do you have on the team?

The evidence of “movement” is that you are in a place that is measurably different from a place you were before.  So, we have to start by identifying where we are now.

This can be measured in many different ways:

  • Where are you educationally?
    • 8th grade?
    • 12th grade?
    • College?
  • Where are you in your career?
    • 1st job?
    • Supervisor?
    • Manager?
    • VP?
    • CEO?
  • Where are you in your finances?
    • Lots of debt?
    • Little debt?
    • No debt?
    • Paying all bills?
    • Paying some bills?
  • Where are your retirement savings?
    • What savings?
    • I’m started!
    • I’m in good shape!

Some things are more difficult to measure in units, but you can do the same kind of analysis for things like:

  • Personal growth
  • Spiritual growth
  • Personal relationships
  • Work relationships

But, you need some way of identifying your current location so that you can measure (or estimate) the distance you’ve moved by the next measurement point.

Let’s look at the education example to see how today’s physics terms come into play.

If you have a high school diploma (starting point) and you want to earn a college degree (ending point) you can figure the distance you need to travel.  Deciding on your major will give you both a distance and a direction.  Then you need to determine the “time” that you will need to get there.

  • Associates Degree (distance) in Physics (direction) typically takes 2 years (time)
  • Bachelors Degree in Physics typically takes 4 years
  • Masters Degree in Applied Physics we’ll say takes 6 years

Now that you know how far you need to travel, the direction you need to go and the amount of time it normally takes, you could figure out the velocity that most people travel on this trip.

What if you accelerated quickly?  The times given above assume a constant velocity (acceleration = 0) with a course load of 12-15 credit hours per semester.  What if you took 18+ credits for just the first semester or two?   Then you could reach our destination in less time, even if you only took 12-15 credits every semester after that.  

What if you were working full time and could only take 6-9 credits in the first few semesters?  You would start out slower than most (lower acceleration) and it would take you longer than most to finish, even if you took 12-15 credits later on.

Here is where it gets interesting…

What if you took 12-15 credit hours every semester, but half of your classes didn’t count toward your major or electives?   Your speed would still be “12-15 credit hours/semester”, but your velocity would not.  Your velocity was changing because your “direction” was all over the place.  Remember, each time you change your direction it requires acceleration, even though there was no change in speed.  And whenever you have any acceleration (positive or negative) that means a change in velocity.

To be more productive, sometimes you may not need to speed up;   You may just need to change your velocity (direction)!  But that still requires acceleration.

Before reading this post, would that sentence have made any sense to you? 

Imagine, slowing down and getting to your destination sooner!  

What would this look like in the area of personal growth?  

Let’s imagine that today you are “located” in a place where you struggle to get important things accomplished by the end of the day.  Your day job eats up all of your time from 7am (start your commute) until 7pm (arrive back home), then dinner, an hour or two to relax or spend time with friends or family, and then you try to fit in these “important things” before bed.  Often you find that you are too tired or distracted to focus and get them done.  So, the last 1-2 hours of your day are sort of wasted.

What if you were to get up earlier and do some of those important things first?  But getting up 1 or 2 hours earlier would be tough to do right away.  So, each morning over the next two weeks you go to bed and get up just 10 minutes earlier.  After 12 days, you have moved those 120 minutes to the start of your day and are getting to those “important tasks” first.  Nothing else in your day has changed.  

You have the same number of non-sleeping hours in a day (elapsed time), but are getting more done, (greater movement).  You “accelerated” your start time (getting up earlier), and that changed your direction (velocity) AND your speed increased!

I can attest to this personally.

After reading John Maxwell’s best-selling book “15 Invaluable Laws of Growth”, I made some of these changes in my life.  My wife, Michelle, saw the positive effect and then she read the book and also made similar changes.  We started to get up earlier so that we could get the most important things (to us) done first. That led us to make other small changes.  We joined Weight Watchers and started to eat a much healthier diet (and I got a physical trainer).   4 months later, I’m almost 40 pounds lighter, feel better and stronger, and I’m getting more done in my days.  It required an “acceleration” in our lives.

We put the pedal to the metal and used a lot of acceleration to change several of our velocities at the same time.   But that isn’t always the best plan.  You need to find the acceleration that you can live with and maintain.  Just like with a car, if you accelerate too quickly you can just spin the tires and go nowhere, then get exhausted and quit.

Now, back to the hamster I mentioned in my title.   (*note*, I readily admit that I’m playing fast-and-loose with the words “speed” and “velocity” in this case.  So, just follow me through the life application and not the physics.)

As the hamster spins around on its wheel, it seems to have a great amount of speed.  But since its starting point is the same place as his ending point, thus no direction, we know that there is no velocity.  How often do we feel like that hamster?   Lots of speed, no velocity – no measurable change of location (i.e. movement). 


In my previous blog I asked you to make a list of the things in your life that have “mass”.  Things that “matter” to you.   This time I would ask that you start to think about changes that you might like to make in your life.  Which of the items  on your list need to moved from where they are today to someplace new.  

Consider how far that move will be (distance)

Consider how much time it might take to make that change (average velocity)

Consider how quickly you could get started (initial acceleration)

Maybe you have something already moving in your life, but it needs a new direction – that still requires a change in velocity which requires some kind of acceleration.

Once you have a few items on your list, identify at least two ways that you could accomplish that change.  What kind of “acceleration” would you need to make that change in velocity?

In a future post, we’ll talk about FORCE and how it energizes all of this change.

Recommended Videos:

Check out this awesome video with a song by “They Might Be Giants” on the relationship between speed, velocity and acceleration

Check out this video from “2 Minute Classroom” for a very easy follow lesson on the relationship between today’s terms


I want to keep the science in these posts relatively simple, so my definitions above assume that the passage of time is constant, but that isn’t always true.   I don’t fully understand the science behind it, but it is believed that there are different conditions in the universe where the passage of time isn’t the same.   Which is actually a pretty amazing idea!

We’ve talked about the relationship between movement, velocity and acceleration being a function of time, but if “time” isn’t the same at your destination as it was at your starting point these calculations get incredibly difficult.

I bring this up to make this point…  

Do you “feel” like time is moving faster or slower for you now than it did 5 years ago?   10 years ago?

If so, then the same amount of effort (force, energy) that you were using back then to achieve certain acceleration or velocity may not produce the same results today.


   Mind blown!   

Enjoy the rest of your day. 

1 thought on “(3) “Hamster Wheel”: Lots Of Speed… No Velocity”

  1. “Imagine, slowing down and getting to your destination sooner!” – a very counter-intuitive principle. It’s easy to be busy – to have a lot of motion – but it’s much harder to be intensely focused and be busy about the right things.

    It reminds me of an incident in a comic I once read: long story short, the characters were looking for a missing person. The main characters were working with a group of “reformed criminals” to find the missing person. Everyone took off to search different locations, except the boss, who slowly headed to his destination.

    When word came in that the missing person was at X location, the boss never even changed direction – he had been heading there all along. When we know what we want and what it takes to get there, and have the courage to focus on what matters and ignore the distractions, we can get to our destination in record time – even when we slow down!

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