An 8 kg block is pushed across a horizontal surface by a horizontally oriented force whose magnitude varies in time. The instantaneous power supplied by the pushing force to the block is P subscript p u s h end subscript open parentheses t close parentheses equals open parentheses 4 straight W over straight s cubed close parentheses t cubed If the block starts at rest at t = 0 s, what is the displacement (in m) of the block after 3 s?

4.5 m

Explanation:

We are given that

Mass of block,m=8 kg

Apply work energy theorem

Where

Integrating on both sides

integrating on both sides

Substitute t=3 s

Hence, the displacement of the block after 3 s=4.5 m

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.