Calculate Work and Crate Speed in Astronaut's Space Station Maneuvers

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The discussion revolves around calculating the total work done by an astronaut on a crate in a space station and determining the crate's final speed. The astronaut first applies a force of 250 N to accelerate the crate over 5 m, resulting in 370 J of work. Afterward, the astronaut applies a force of 220 N to decelerate the crate over 4 m. To find the final speed, the net work done on the crate must be added to its initial kinetic energy, using the equation for kinetic energy (KE = ½mv²). The participants are focused on how to correctly apply these principles to derive the final speed of the crate.
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Homework Statement



A crate with a mass of 120 kg glides through a space station with a speed of 2.5 m/s. An astronaut speeds it up by pushing on it from behind with a force of 250 N, continually pushing with this force through a distance of 5 m. The astronaut moves around to the front of the crate and slows the crate down by pushing backwards with a force of 220 N, backing up through a distance of 4 m.

What is the total amount of work done by the astronaut in these two maneuvers? (I correctly calculated this to be W = 370J)


After these two maneuvers, what is the speed of the crate?


Homework Equations



Kf - Ki = work

The Attempt at a Solution



I found the work, but need the speed. I just can't figure out how to pull the velocity out of that correctly
 
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I found the work, but need the speed. I just can't figure out how to pull the velocity out of that correctly
If you want speed then what was the KE of the object initially?

How much net work did the astroworker do? If you add that to the object's energy, that's the final KE and Ke = ½mv²
 

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