What are 2 uses for this tiny electromagnet?

It's not necessarily so tiny.  We can't really tell, but look at the size of the paper clips.

Anyway, it doesn't really matter.

If you actually HAD this machine, it could be very useful, in EXACTLY the situation shown in the picture:  Your lab partner is a clumsy klutz ... during the electromagnet experiment, s/he emptied a whole 2-pound box of paper clips all over the floor of the lab, and the teacher wants every one of them picked up, RIGHT NOW !  Your partner gets down on knees and starts picking the clips up off the floor, one at a time.  But YOU have this wonderful machine that you've been working with in the lab !  YOU get down on your knees, switch it ON, and you slowly wave the coil with the iron core back and forth, a few inches above the floor.  All of the paper clips slide over to you and snap themselves onto the electromagnet, just like you see in the picture.  THEN you hold it over the empty box and switch the power OFF.  All the clips fall off of the magnet and into the box, and the teacher immediately gives you an A for that lab.

Or ... you could use it as a real-world teaching tool. Just carry it with you everywhere you go for a whole day, and try it on everything.  Whatever you do all day, switch the electromagnet ON, and see what it sticks to and what it doesn't bugs, spoons, books, toilet paper, smartphone, phone in the house, newspaper, car steering wheel, windows, computer, computer mouse, real mouse, pencil, earbuds, vape smoke, your blue hoodie, skateboard, scooter, tires, rocks, water, goldfish, donuts, Coke, Pepsi, raw burger meat, cooked burger meat, the bun, nails, nickels, dimes, quarters, pennies, dollar bills, coins from other countries, ketchup, drumstick from a drum, drumstick from a chicken, your baby brother, a notebook, a compass, the schoolbus, a plastic trash can, a bathroom faucet, a kitchen faucet, etc. etc. etc.  Find 10 or 20 things that DO stick to it when it's ON, and 10 or 20 things that DON't.  You'll learn so much that by the end of the day, you'll be able to LOOK at something and TELL whether it'll stick to the electromagnet or not, without even trying it.  Your friends will be amazed.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.