Speed of Driving
It's a little stressful when you're driving exactly the speed limit (of course, I would never go beyond the posted speed limit) and someone zooms by you at 10, 15, or sometimes 20+ miles per hour. As a bonus, these people will usually weave through traffic too. What's so important that you'd risk your life, and several other peoples', to save some time? Maybe, man's gotta poo. Who knows? But something I do think about, is how much time are they actually saving, assuming they don't get into a crash or stopped by the police?
A Lawful Example
Let's assume a 30-mile commute, separated into 3 segments: Pre-highway, highway, and post-highway. Each one of these segments has a uniquely defined distance and speed. For this example, let's say that both the pre-highway and post-highway segments are 5 miles each and have speed limits of 35 miles per hour, and the highway segment is the remaining 20 miles and has a speed limit of 65 miles per hour.
The off-highway segments will have traffic lights, so the average speed for those will be lower than 35 miles per hour, maybe around 30 miles per hour. From here we can calculate the total time for this trip.
Our speed (velocity) is given in miles per hour, so \(t\) is measured in hours. Let's convert to minutes by multiplying by 60.
| Segment | Distance \(\Delta x\) | Speed \(v\) | Time \(t\) |
|---|---|---|---|
| Pre-highway | 5 miles | 30 mph | 10:00 min |
| Highway | 20 miles | 65 mph | 18:28 min |
| Post-highway | 5 miles | 30 mph | 10:00 min |
The total commute time for this example is 38:28 min.
Speeding Up
It's more difficult to speed off-highways, so let's say someone speeds at 10 miles per hour above the speed limit on the highway. How much time do you think this would save? Take a guess before reading on.
The off-highway durations would be the same, so the only difference would be the time spent on the highway.
That's right, speeding by 10 mph saves you 2 minutes and 28 seconds. The total commute time drops to... 36:00 min.
Outright Breaking The Law
Now what if you're speeding at 20 miles per hour above the posted speed limit on the highway? Crawling at a snails pace of 85 mph is a common occurrence in California.
Adding another 10 miles per hour saved less than 2 minutes this time! The total commute time for this trip is 34:07 min.
Just for funsies, if you were speeding at 30 mph above the speed limit (that's 95 mph, by the way...) the total trip would still take you 32:38 min, which is less than another minute and a half saved.
Kinetic Energy
Now we see that speeding up has diminishing returns on time saved. What about kinetic energy? What is kinetic energy? It's the energy stored in your vehicle while it's moving. The higher the kinetic energy, the harder it is to stop moving, and the harder it will hit something on impact. It's defined by this formula. I added a factor of \(0.09\) to convert all US units to metric.
Assume we're in a 3,000 lb car. This is actually pretty lightweight for today's standards.
| Mass \(m\) | Velocity \(v\) | Kinetic Energy \(KE\) | TNT Equivalent |
|---|---|---|---|
| 3,000 lb | 65 mph | 0.57 MJ | 136g (5oz) |
| 3,000 lb | 75 mph | 0.76 MJ | 181g (6oz) |
| 3,000 lb | 85 mph | 0.98 MJ | 233g (8oz) |
| 3,000 lb | 95 mph | 1.22 MJ | 291g (10oz) |
Our kinetic energy increases quadratically with our speed increases. Hitting something at 85 mph in this car is like blowing up half a pound of TNT!