Acrate on a motorized cart starts from rest and moves with a constant eastward acceleration ofa= 2.60 m/s^2. a worker assists the cart by pushing on the crate with a force that is eastward andhas magnitude that depends on time. according to f(t) = (5.40 n/s)t. what is the instantaneouspower supplied by this force at t= 4.70 s

To obtain the power, we first need to find the work made by the force.

1) To calculate the work, we need the next equation:

So the force is given by the problem so our mission is to find 'dx' in terms of 't'

2) we know that:

So we have:

Then:

3) Finally, we replace everything:

After some calculation, we have as a result that the work is:

161.9638 J.

4) To calculate the power we need the next equation:

So

P = 161.9638/4.7 = 34.46 W

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.