What is the final velocity from given work, mass, initial velocity, and time?

AI Thread Summary
To find the final velocity given work, mass, initial velocity, and time, the user is applying the work-energy principle, specifically W = Fd and W = change in energy. They attempted to derive a formula for final velocity (vf) but faced algebraic difficulties, leading to an incorrect solution of vf = 230.84. The confusion arose from substituting distance (d) and interpreting the equations correctly. Clarification on the algebraic steps and proper symbol usage is needed for accurate problem-solving. The discussion highlights the importance of understanding the relationships between work, force, and motion in physics.
cretin66
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Homework Statement


I am trying to find the final velocity from the given data
Work - 3000J
Mass - 1/2d (d = distance travelled)
Initial Velocity - 7m/s
Time - 7 seconds

Homework Equations


W=change in energy
W=Fd

The Attempt at a Solution


W =work
F=force
m=mass
a=acceleration
d=distance traveled
vf= final velocity
v0=initial velocity
t=time
Attempt #1
W=Fd
W=mad
3000=1/2d[2]a
W=1/2(vf + v0/2t)[2](vf - v0/t)
and by solving this equation...
vf[3] + 7vf[2] - 49vf - 343 = 3000
I've tried putting everything equal to zero and using a graphing calculator to solve for the x-intercept, and using a check i found that i had the wrong answer, it's possible that my algebra was done improperly, or I am approaching the problem the wrong way, please help.
The answer i got was vf = 230.84
 
Last edited:
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cretin66 said:
W=1/2(vf + v0/2t)[2](vf - v0/t)

How did you get this equation?
 
because d=vf + v0/2/t, i just replaced all the d's in the equation with this value
 
I guess I'm having a little bit of confusion with your symbols. [2] is squared, and m = 1/2d = d/2 or is it 1/(2d)?
 
1/2d=d/2, sorry I was in a hurry, and yes [2] is squared
 
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