Chapter 1: The Day

'Good morning, dreary sky of little to offer. I hope you do not piss on me as I wait for the train.' thought Nikolai as he drank his tea. It offered him warmth and strength to press on through the day, which he otherwise lacked. His older brother had been away, for a heart surgery and recovery process. He was a great nurse and so he was needed Shouldn't take too much longer, but it was taxing Nikolai already. 

Whenever Nikolai didn't know what was going on in any area of importance, his mind would race to the worst outcome. What if they died? What if they were kidnapped? It was always that heavy, paralyzing fear that slowed his heart to unsustainable levels. One day he'd get over it, but it seemed so far from now.

Regardless, he didn't have time to eat anything fulfilling besides a small piece of crusty bread in the cabinet. But it would fulfill him for the time being. Gathering up his belongings, he headed off to the train station. Bryansk No.3 was a simple station of simple structure, but the inside was ornate as many subways were. A true people's palace it was.

He liked the wait today, because he found cover. The open design was due to bad design. The godforsaken architect forgot he was designing an aboveground station and so provided no top at all, except for the very edges. He opened up his old smartphone and began scrolling aimlessly, just looking for a small hit of dopamine before the train. 

He did find a couple, lucky guy today. But eventually, the telltale whistle indicated to him that the train was coming to the station and he needed to get going from his little nook. Of course, the grey sky cared very little of Nikolai's request, perhaps because it can't hear or something similar. He began his dash to the train, wanting his favorite window seat in the last compartment. But the ground decided that No, he was not destined for that seat, and one stray pace later he was flying through a crowd of people.

Unable to control his short-lived flight, he angled to the right a bit, narrowly missing a burly gentleman and a kid no older than 11 who would have his first independent ride to school today. Through the crowd he went as time seemed to slow down, until he eventually found his target, a young woman. 

The two of them tumbled down, hitting the cold, hard bricks of the floor before rolling a bit more, without control. Both tried desperately to stop and find a handhold, though no such luck was granted to them. After the last roll, some sort of amazing or terrible look had Nikolai on top of the woman, gripping her breasts.

"Please, I'm sorry! Those weren't my intentions! I slipped and fell!"

"That's what all of them say, huh. Liar!"

"I'm not lying! Look at all the force I hit you with!"

"Okay, so you're a stupid liar. No way!"

"No, please! I beg you, I didn't mean it!"

"Okay, fine. You didn't. Now don't make me miss my train." The woman scampered off and Nikolai followed, promptly sitting as far away as possible from her.

'What a day.' Nikolai thought to himself. 8:30 and he already touched the breasts of a beautiful woman? This had to be some sort of either humiliation or some reward from God, otherwise it made no sense. At 17 Nikolai hadn't even had his first kiss or first girlfriend yet, so that was a large new development in his portfolio. Right now, he was too focused on the Duchess from a popular game to care.

The train eventually stopped at his station, a block or so from his school. He left the train quickly and safely, not hoping for another incident. 'Dry asphalt, dry life events.' He thought to himself, as the rain had cleared and left a slight, misty fog obscuring the sign. It was the same one which he passed every day, that of Bryansk Secondary No.3. The brick building, first constructed in 1935 and renovated in 2007, stood tall and imposing.

Especially so today considering his exam in Physics Honors was today. Solving equations for the motion of an object is somehow less fun than watching paint dry yet more tedious than applying four more coats after with none but a tiny watercolor brush. Not to mention, it was closed notebook and hard as hell.

Despite this, he was the one who chose physics over biology. Oh, it'd be so much better to cut up frogs and mice than solve F=ma for the most obscure problem ever, without a calculator. "You won't always have a calculator in your pocket."

That was his favorite phrase as an old-school teacher who'd been around for all of 35 years teaching unruly 10th graders how to do physics equations, and it certainly took its toll on the man. He was frail and very unassuming, his voice having a constant tinge of off-ness if you could describe it like that.

Nikolai walked into the classroom and dropped his stuff by the bag dropoff, for cheating prevention. All he received was the test, four sheets of scratch paper, and two sharp pencils. Classmates followed him into the room and eventually Mr. Ryabinin walked to his desk and stood up vs. sitting. That's when shit got real.

"Alright, students. Today, we should see if you learned anything at all this unit, and I don't know about my estimates about you. I hope you all do well but 35 years in the field tells me I am not always right with you. I guess we'll see." He readjusted his spectacles and continued, "As per the standards, I will read to you this booklet before we begin the test. "

He pulled out thin booklet of about ten pages and started on the content. Nikolai had heard this many times before as it was mandated for all academic testing within region limits.

"Today all students will be taking the Physics Honors... You are only allowed the equipment provided to you by your teacher... you cannot have anything else on you even if you are not using it... Cheating will result in a mark on your record and a zero... The test will end at..."

He continued through the tedious booklet until he reached the teachers' guide and promptly closed the book and instructed the students to get on it. 'Well, here goes nothing', thought Nikolai. He worked through the first few equations, plugging in whole numbers and else. Then on the theory side, he struggled through the multiple choice questions. Once he got to physicists, he made it look like a lightning round. But then, the last question. 

A roller coaster car with a mass of 900 kg travels along a track with three different sections - a long straight uphill section, a loop-the-loop section, and a curved downhill section before returning to the start.

In the straight uphill section, the car accelerates at 2.5 m/s2 over a distance of 120 m. In the loop-the-loop section, the loop radius is 40 m. In the curved downhill section, the radius of curvature is 80 m and the car travels through an angle of 1.2 radians.

Using Newton's 2nd law (F=ma) and assuming friction is negligible:

Determine the normal force on the car in the straight uphill section

Calculate the normal force on the car at the top of the loop when it is inverted

Find the speed of the car at the bottom of the curved downhill section.