# Finding speed given force and distance

1. Oct 18, 2009

### fattydq

Starting from rest, a constant force of 45 N acts on a 67 kg skier over a distance of 8.1 m. What is the skier's final speed in m/s^2?

Now I'm assuming since force is distance times acceleration, I can take 45 and divide it by 8.1 to find the acceleration. But even still, then I will have distance and acceleration, but no unit of time to take into account. Any suggestions? This is my last post of the day I swear! : P

2. Oct 18, 2009

### 206PiruBlood

Force is NOT distance times acceleration, it is F=ma.

Have you learned the work energy theorem? Remember that the work is force times distance or W=Fd. According to the work energy theorem this is also equal to the change in kinetic energy.

3. Oct 18, 2009

### fattydq

Right, mass times acceleration, not distance times acceleration, my mistake. I still don't understand how, given the figures I'm given, I can use Work equals force times distance to find SPEED?

4. Oct 18, 2009

### 206PiruBlood

These are the relationships you need to know to solve this.

W=Fd
$$w=\Delta E_k$$
$$E_k=\frac{1}{2}mv^2$$

Once you find the work you have simultaneously found the change in kinetic energy. Assuming the skier starts at rest, then the change in kinetic energy is the total kinetic energy. Solve for velocity.

5. Oct 18, 2009

### fattydq

So 45 times 8.1=364.5
364.5=\Delta E_k[/tex]
And thus 364.5=1/2 (67) times velocity^2 which turns into
729=67*V^2
729 Divided by 67 =10.88 m/s^2 which is velocity squared, taking the square root of that gives me

3.298575 m/s^2

Is this correct?

6. Oct 18, 2009

### 206PiruBlood

yep yep :D

Well the units should just be meters per second, yours represents acceleration!

7. Oct 18, 2009

### fattydq

Strange...on my worksheet it says "What is the skier's final speed in m/s^2?" So I just assumed those were the units...

8. Oct 18, 2009

### fattydq

Well regardless, thanks a lot for the help! : )

9. Oct 18, 2009

### the pro

nah that is wrong i now u need to now this f=m x a so we dont now a so we do it like this f=m x a /m then we go like this to a=f/m and btw mos je i deqanit

10. Oct 18, 2009

### fattydq

I'm going to go ahead and ignore your post since half of it isn't even in proper English...no offense...And beside it asks for speed not acceleration...

11. Oct 18, 2009

### 206PiruBlood

Well meters per second squared is an acceleration and meters per second is a velocity. Im assuming its just a typo.

12. Oct 18, 2009

### fattydq

Yeah, me too, I'm assuming my professor just meant m/s. I'll have to bring it up to her in class tomorrow.