Anime Theory: Haruyuki Should Have Just Been Hit By the Car

I Love Accel World. Say what you will about its writing, but I cannot put it below rank 14 in my personal anime list. Its characters are unique, its story is engaging, but that's not what I'm here for. Today, we will be looking at Accel World episode 4 from the eyes of a physicist. Get out your kinematics notes, because today we will take a look at why Haruyuki should have just been hit by the car.

The Background

Haruyuki and Kuroyukihime (great names by the way) are out in front of their friendly neighborhood WcDonalds discussing their relationship. The drama here is Kuroyukihime got jealous when he "cabled" (connected their brains with a cable like in the image) with his childhood friend Chiyuri. Haruyuki takes the jealousy too seriously and starts acting passive aggressive. Right after their spat, they hear, then see a car veering off the road towards them. At this point, it's important to know what's special about the series. The story centers around a game that speeds up human consciousness to 1000x normal speed, and can allow movement at 100x normal speed. Now, let's get into the scene in question

The setup

Kuroyukihime's strategy is to speed up to 100x speed and push Haruyuki out of the way of the incoming car. The best image I found to display their distance made it seem like they were about a meter apart. Due to Kuroyukihime's hospitalization and car crash data, I deduce that the car was going at about 35 km/h, 22 mi/h, or 9.7 m/s. The location of the car is harder to place. I'm guessing it was about 3-4 meters from the couple when they accelerated. The time span is much easier: the whole event takes place from 10:18 to 16:44, with the push taking place from 15:30 to 16:44. This means in the whole time they spend chatting, (6*60+26)/1000 = .386 seconds pass. The time spent pushing is a modest 74/1000= .074 seconds. Contact is made with Haruyuki at 16:17, leaving only .027 seconds for him to move. From the angle of the car's approach, Haruyuki would have to be pushed 0.9 meters to completely dodge it. Haruyuki's bio states he is 56 kg, and Kuroyukihime is 48 kg.

The calculations

The first threat to calculate is the car. They are extremely lucky because in this amount of time, the car can move 3.7m, just within my estimate, so the time frame is realistic. However, the car is not actually the most dangerous object flying around. Assuming there is no need for acceleration buildup, Haruyuki would have to move at an average speed of 33 m/s or 74 mi/h. Forget that 22 mi/h car. Now Haruyuki has to worry about being flung into a wall at more than 3 times that speed. If you assume perfectly efficient acceleration, he would have to be accelerating at 252 gs. The most any human has ever survived is 46 gs, but maybe this super short exposure time makes it OK; I don't know. What is more interesting is the energy needed to push them that fast. It takes 57,800 J to push the two of them to 33 m/s. That may sound like a lot, but it's actually just the amount of energy in a packet of sugar. Human muscle efficiency is about 25%, so it would take 231,200 J or 4 packets of sugar to actually do this. The definition of power is energy divided by time, so if we do 231,200 J / .074 seconds, we get 3.1MW. This is 32,000x the normal energy usage of a human (97W), and 2,500x the electricity usage of your average home.

The anime also seems to be lying about how much it can speed up physical movement. to push 104 kilograms at 252 gs, Kuroyukihime would have to have to exert enough force to match the weight lifting world record, even taking into account the 100x boost.

The conclusion

If Kuroyukihime were to push Haruyuki, she would first be torn apart by torque forces (which are much harder to calculate, so I didn't), and by using enough energy to power your house for 3 minutes, she would accelerate both Haruyuki and herself to more than three times the speed of the incoming car, at a rate 4.5 times faster than anyone in human history has survived, likely killing them both. That guy running off to the left is also screwed when Haruyuki goes flying at him at 74 mi/h, assuming he stays in one piece. Honestly, a 35 km/h crash only has a 8% chance of fatality anyway. I would just risk it. And this is why Haruyuki should have just been hit by the car.