physics of acceleration

photo credit: jurveston

I am sure that even without this explanation you understand what acceleration is – I mean it is more than likely that you have been in an accelerating car before.  But what would you say if I asked you to describe it to me? Would you say “It’s when you speed up”? Or, maybe “It’s when you go faster and faster and faster”?

You have to admit, even though you “get” what it is, acceleration is pretty hard to describe.  ”Speeding up” and “faster and faster” work in general conversation but aren’t very mathematically stable.

So, in order to describe what acceleration is I have to back WAY up … as you’re reading you’re probably gonna be nodding along thinking that you know all this … and I’m not saying you don’t … but I have to explain it all before I can get to the part you may not know which is the physics of acceleration.  In short, bare (or is it bear?) with me. (Hey… I said I’m good a physics – language, not so much).

What is Acceleration?

The easiest way to discuss acceleration is to talk about something you are all very familiar with – cars.  Specifically we are going to be talking a lot about the speedometer.

When you are at a stop light, the speedometer of the car reads 0 miles/hour.  When the light turns green, you step on the gas and the velocity (or speed) of the car begins to increase over time and as you do that, the speedometer slowly creeps up.  That gradual increase in speed is acceleration.

If you were to time the speedometer you’d see that for every second that passes while you’re accelerating, you are gaining a certain amount of speed.

Let me be super tedious and walk through an example …

  • At the stop light, you’re speedometer reads 0 miles/hour
  • The light turns green and you step on the gas
  • One second later, you are going 10 miles/hour
  • One second after that, you are going 20 miles/hour
  • One second after that, you are going 30 miles/hour.

Obviously you are accelerating because you are “getting faster and faster” but, mathematically and physically speaking, what we need to know is at what rate are you “getting faster in faster”?

In the example, it appears that every second that passed, we gained an extra 10 miles/hour in speed and….

…. we could flip that sentence around to say: 10 miles/hour were gained every second….

…. so mathematically we could show that as: 10 miles/hour/second (10 miles per hour per second).

Makes perfect sense right!

Ok … here’s where it starts to get confusing.

What if instead of a car, we were in a rocket ship that accelerates WAY faster than a car – so fast that instead of measuring it’s speed in miles/hour like a car, the rocket’s speed is measured in miles/second.  If we redo the example above with the rocket ship it would look like this:

  • On the launch pad, the rocket’s speedometer reads 0 miles/second
  • The ignition is fired and TAKE-OFF
  • One second later, the rocket is going 10 miles/second
  • One second after that, the rocket is going 20 miles/second
  • One second after that, the rocket is going 30 miles/second.

Similar to the car you could say, based on these numbers, that 10 miles/second were gained every second and, also similar to the car, you could express that mathematically as 10 miles/second/second (10 miles per second per second).

But here’s the clincher!

Physicists have a un-explainable need to re-arrange and shorten everything and this is one of the things they just couldn’t leave alone.   In physics, it is perfectly acceptable to express the car’s acceleration as 10 miles/hour/second but the rocket’s acceleration would always be shown as 10 miles/s2…. yup, 10 miles per second squared and POOF! all of a sudden something that a moment ago made complete sense to you is instantly confusing!

What the heck is a mile/s2?

The answer is: It is the same thing it was before … it’s a mile/second/second except now it’s shorter to write.

I think I better stop here for now and let that marinate in you’re brain for a little bit… when you’re ready come check out part 2 of this post.