A60 kg man is sitting on the floor of an airplane 8000 m high traveling at 850 km/hr. how much total mechanical energy does he have relative to the reference frame of the plane?

Relative to reference frame of the airplane he's sitting in:

-- Gravitational potential energy = (mass) (gravity) (height)

His height above the airplane is zero, so his GPE is zero.

-- Kinetic energy = (1/2) (mass) (speed)²

His speed relative to the airplane is zero, so his KE is zero.

Mechanical energy = (potential energy) + (kinetic energy)

Mechanical energy = ( 0 ) + ( 0 )

The poor fellow's total mechanical energy is zero .

force tends to be low and long diustance masses are high

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.