The large piston in a hydraulic lift has an area of 250 cm2. What force must be applied to the small piston with an area of 25 cm2 in order to raise a car of mass 1500 kg?

Explanation:

Given that,

Area of large piston,

Area of small piston,

Force applied to large piston,

It is required to find the force applied to the small piston. The pressure in each chamber must be equal so, that,

F₂ is force applied to smaller piston

So, the force of 150 kN must be applied to the small piston.

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.