Work and final velocity with two opposing forces on a 70kg mass

[magma_saber]

Homework Statement

A 70kg mass is in a space and moving at 2.5 m/s. You push it with 200N for 4 m. You then move to the front of the mass and push it backwards with 170N for 3 m.

What was the total work done?
What was the final velocity?

Homework Equations

W = rest energy + F₁*r - F₂*r

The Attempt at a Solution

rest energy = 1/2*70*(2.5)² = 218.75
F₁*r = 200*4 = 800
F₂*r = 170*3 = 510
W = 218.75 + 800 - 510 = 508.75 J

How would i get the final velocity?

 

[LowlyPion]

How would i get the final velocity?

Initial KE + Work = Final KE

Initial ½mv² + W = Final ½mv²

 

[magma_saber]

so its 218.75 + 800 + 510?

 

[LowlyPion]

so its 218.75 + 800 + 510?

Perhaps I should rephrase that since you want to plug in numbers literally without thinking about the signs:

Initial ½mv² + ΔW = Final ½mv²

Btw your initial calculation incorrectly includes the initial KE in the ΔW they asked you to find.