Work required for truck up a hill problem

[gigglin_horse]

Homework Statement

"Is more work required to bring a fully loaded truck up to a given speed than the same truck lightly loaded? Defend your answer"

Homework Equations

I put:
Work = Force x distance
Distance = speed x time
As speed in a common factor, we take it out
Work = Force x time....Is this correct so far?

So the work is the same.
Small force, long time, or short time, big force.


But doesn't work = change in KE?
so W = 1/2 m x v^2
...So the greater one does require more work?

I don't know...

Help me please!

The Attempt at a Solution

 

[Doc Al]

I put:
Work = Force x distance
Distance = speed x time
As speed in a common factor, we take it out
Work = Force x time....Is this correct so far?

No, not correct. (If work = force*distance, which it does, how can it also equal force*time? The units won't even make sense. FYI: force*time = change in momentum, not work.)

So the work is the same.
Small force, long time, or short time, big force.

No.

But doesn't work = change in KE?

Yes!

so W = 1/2 m x v^2
...So the greater one does require more work?

Yes!

 

[gigglin_horse]

Brilliant, thank you
=]