physics, short, silly, thought experiment

Late for Work

I work a pretty standard 9-to-5 job. Now I know 9 to 5 is actually pretty cushy hours. I’ve got friends whose hours are more like 6 AM to whenever-it’s-done. But my lizard brain won’t get the message that 9 AM isn’t that early a start. Apparently, my brain thinks that getting up at 8 AM is the same as getting up at 3:30 and having to walk ten miles to work (in the snow, uphill both ways).

Luckily, I really don’t like being late, so I manage to be on time by pure stubbornness. But sometimes, it’s a pretty close shave. And while I was driving to work the other day, I got to wondering just how late I could leave the house and have any chance of getting to work on time.

My commute to work is 23.1 miles (37.2 kilometers). According to Google Maps, it should take about 39 minutes, which seems about right. That means an average speed of 35.5 miles per hour (57.2 kilometers per hour). Considering at least half that distance is on the highway at 70 miles per hour (113 km/h), that seems a little slow, but to be honest, there are a lot of traffic lights and weird intersections in the non-highway section, so it probably works out.

But the question remains: how quickly could I possibly get to work? And, therefore, how late could I leave the house and still get to work on time?

The most obvious solution is to convert myself into a beam of light (for certain definitions of “most obvious”). Since there are no vacuum tunnels between here and work, I can’t travel at the full 299,793 kilometers per second that light travels in vacuum. I can only go 299,705. Tragic. Either way, by turning myself into a beam of light, I can get to work in 0.124 milliseconds. So as long as I’m dressed and ready by 8:59:59.999876 AM, I’ll be fine.

Of course, there’d be machinery involved in converting me to light and then back into matter again, and considering what a decent internet connection costs around here, it ain’t gonna be cheap to send that much data. So I should probably travel there as matter.

It’d make sense to fire myself out of some sort of cannon, or maybe catch a ride on an ICBM. The trouble is that I am more or less human, and even most trained humans can’t accelerate faster than 98.1 m/s^2 (10 g) for very long without becoming dead humans. I am not what you’d call a well-trained human. Sadly, I don’t have easy access to a centrifuge, so I don’t know my actual acceleration tolerance, but I’d put it in the region of 3 to 5 g: 29.43 to 49.05 m/s^2.

Figuring out how long it’ll take me to get to work with a constant acceleration is pretty simple. We’ll assume I hop in my ridiculous rocket, accelerate at 3 to 5 g until I reach the halfway point, then flip the rocket around and decelerate at the same pace until I arrive. And since the math for constant acceleration is fairly simple, we know that

distance traveled = (1/2) * acceleration * [duration of acceleration]^2

A little calculus tells us that

duration of acceleration = square root[(2 * distance traveled) / (acceleration)]

Of course, I have to divide distance traveled by two, since I’m only accelerating to the halfway point. And then double the result, because decelerating takes the same amount of time, at constant acceleration. So, at 3 g, I can get to work in 71.2 seconds (reaching a maximum speed of 1,048 meters per second, which is about the speed of a high-powered rifle bullet). So, as long as I’m inside my rocket and have the engines running by 8:58:48.8 AM, I’ll be at work exactly on time. Though after struggling with triple my usual body weight for a minute and twelve seconds, I’ll probably be even groggier than I usually am.

I have no idea if I can even physically tolerate 5 g of acceleration. I mean, I’m hardly in prime physical condition, but I’m not knocking on death’s door either. But I’m gonna venture to guess that anything above 5 g would probably kill me, or at least leave me needing a sick day by the time I actually got to work, which would defeat the whole point. At 5 g, I only need 55.06 seconds to get to work, reaching a maximum 1,350 m/s. So, if I’m in my rocket by 8:59:04.94, I’m golden!

Of course, that was assuming that, for some reason, I do all my accelerating along my usual route. And frankly, if you’ve got a rocket that can do 5 g for over a minute, and you’re not flying, you’re doing it wrong. According to an online calculator, the straight-line distance between home and work is 13.33 miles (21.46 km). Re-doing the math, at 3 g, I can make it to work in 38.18 seconds (meaning I can leave at 8:59:21.82 AM, and will reach 568.1 m/s). At 5 g, I’ll be there in 29.58 seconds (leaving at 8:59:30.42, reaching 936.4 meters per second).

And yet, no matter how quickly I can get to work, I’m still gonna wish I could’ve slept in.

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