Which of the following would cause a fan cart to accelerate the least? - doubling the speed of the fan
- pointing the fan exhaust downward
- tripling the speed of the fan
- pointing the fan exhaust upward

The correct option is;

-Pointing the fan exhaust upward

Explanation:

The fan cart transfers reaction force from the jet of air it blows through the exhaust into motion in the opposite direction of the jet. By pointing the fan exhaust upwards, the direction of motion of the cart is therefore, into the ground. Due to the solid nature of the ground the motion is resisted, and by Newton's first law of motion, a body will remain in motion unless resisted by a force. In the case of the question, the ground is resisting the motion of the cart and the cart will remain at rest and having zero acceleration.

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.