A student approaches the outdoor staircase near Hope Commons, and takes a deep breath before attempting to climb all 30 stairs. At the bottom of the stairs, the student (61.8 kg) is moving at 2.00 m/s; at the top of the stairs the student is tired and only moving at 0.500 m/s. The top of the stairs is 7.50 meters higher than the bottom of the stairs. What is the change in mechanical energy

Change in mechanical energy, ΔE = 4426.425 J

Explanation:

Mass of the student, m = 61.8 kg

At the bottom of the stairs:

speed,

Mechanical Energy at the bottom of the stairs,

The potential energy while the boy was transiting from the bottom of the stairs to the top of the stairs.

Difference in height between top and bottom of stairs, h = 7.5m

At the top of stairs,

Kinetic energy at the top of stairs,

Total Mechanical energy at the top of the stairs,

Change in mechanical energy, ΔE =

ΔE = 550.025 - 123.6

ΔE = 4426.425 J

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.