A spring whose spring constant is 850 N/m is compressed 0.40 m. What is the maximum speed it can give to a 0.5 kg box? Assume there is no friction in the system.

The maximum speed, the box can attain is 16.5 m/s.

Explanation:

According to law of conservation of energy, energy can be transferred from one form to another. So here the spring force is converted to kinetic energy experienced by the box due to the spring.

As we know, that spring force is directly proportional to the square of the displacement and spring constant, the conservation of energy will be give

So, we know that spring constant k = 850 N/m, the displacement experienced by the spring due to compression is given as x = 0.4 m. The mass of the box is given as m = 0.5 kg and the velocity we have to find.

Thus, the maximum speed, the box can attain is 16.5 m/s.

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.