Work Question - Is something missing?

[Sabellic]

Homework Statement

Calculate the work done accelerating a 2.0 kg object from 2.0 m/s to 3.0 m/s.

mass=2.0 kg
Initial Velocity= 2.0 m/s
Final Velocity= 3.0 m/s

Homework Equations

Work=applied force x displacement

The Attempt at a Solution

Correct me, if I am wrong, but don't I need a bit more information to answer this question? This was all the information given to me.

 

[alphysicist]

Hi Sabellic,

Homework Statement

Calculate the work done accelerating a 2.0 kg object from 2.0 m/s to 3.0 m/s.

mass=2.0 kg
Initial Velocity= 2.0 m/s
Final Velocity= 3.0 m/s

Homework Equations

Work=applied force x displacement

The Attempt at a Solution

Correct me, if I am wrong, but don't I need a bit more information to answer this question? This was all the information given to me.

No, that's all you need. The equation you listed is true; however, there is another equation that involves work and velocity. What is it?

 

[Sabellic]

Hmmmm. I don't know. The only thing that I can conjure up is that the work can be equivalent to (mass/acceleration) * (final velocity^2 - initial velocity^2)/2 * a^2

But that doesn't work because i don't have the acceleration.

 

[alphysicist]

Hmmmm. I don't know. The only thing that I can conjure up is that the work can be equivalent to (mass/acceleration) * (final velocity^2 - initial velocity^2)/2 * a^2

But that doesn't work because i don't have the acceleration.

That's so close! But it needs to be:

(mass/acceleration) * (final velocity^2 - initial velocity^2)/2 * a

and so the accelerations will cancel.

Then notice that what you have left is:

(1/2) m vf^2 - (1/2) m vi^2

Does that look more familiar? What are those terms? Once you have that, you will have the important equation that you need to know.

 

[Sabellic]

Oh God you're right. I wrote (mass/acceleration) instead of mass * acceleration. So yes, they would cancel out. Thanks a lot for this. So it will be 5 Joules, I think.

 

[alphysicist]

That's good, but you don't want to have to derive that important formula every time. The way to think about it is

total work = change in kinetic energy

(where total work includes all conservative and non-conservative work).

Since kinetic energy is (1/2) m v^2, you could write down the relation you need right away.