While traveling on a dirt road, the bottom of a car hits a sharp rock anda small hole develops at the bottom of its gas tank. If the height of the gasoline in thetank is 35 cm, determine the initial velocity of the gasoline at the hole. Discuss howthe velocity will change with time and how the flow will be affected it the lid of thetank is closed tightly.

6.86 m/s

Explanation:

velocity of the gasoline through the hole would be

As the height would decrease, the velocity of the flow would decrease.

If the lid of the tank would be closed, the pressure would reduce. so, again the velocity of the flow would reduce.

a lot of it means it can be "burned" for energy and sold at one price. if it is scarce, the price will go up

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.