# Relationship between Velocity, Kinetic Energy and Mass

Tags:
1. Jun 3, 2016

### Nile Anderson

1. The problem statement, all variables and given/known data

2. Relevant equations
i) F=ma=mv/t
ii) E=mv2/2

3. The attempt at a solution
Now based on equation 1 , I have concluded that the velocity gained is inversely proportional to m, and that so is the kinetic energy , I have seen otherwise.

2. Jun 3, 2016

### BvU

How can you conclude that if equation 1 does not contain any distance/displacement at alll ? You need other equations !

3. Jun 3, 2016

### Nile Anderson

Oh hmmmm, x=at^2/2, which means, a=2x/t^2, which means that mv/t=2mx/t^2=F, so does this mean they are independent , I am sorry , I am a little weak.Could you please elaborate?

4. Jun 3, 2016

### BvU

mv/t = F doesn't help you if you don't know how t depends on m.

Would the exercise be easier for you if the text would read:

You have a force $F$ to accelerate a mass $m$ from rest with constant acceleration over a distance $d$. What is the final velocity ?​

5. Jun 3, 2016

### Nile Anderson

I think I see something , the energy gained by the system would be Fd=mad, so this implies that mv^2/2=mad, v^2/2=ad, so this would mean the kinetic energy is independent of m ? Further a=F/m , v=sqrroot(Fd/m), does that mean v varies in an inverse proportion with sqrt(m)

6. Jun 3, 2016

Sir ?

7. Jun 3, 2016

### BvU

Correct
Bingo.

Can you also do the alternative route ? $\ d = {1\over 2} at^2\$ tells you $\ t \propto \sqrt d\$ and you already had $\ mv/t = F$

8. Jun 3, 2016

### Nile Anderson

Thank you so much sir , I get it now

9. Jun 3, 2016

### Nile Anderson

Hmmmmm

10. Jun 3, 2016

### Nile Anderson

Right , I get back the same place sir, thank you so much sir , that helped alot.

11. Jun 3, 2016

### BvU

Hmmm as in "delicious" or Hmmm as in "I don't belive a word of what I read" ?

12. Jun 3, 2016

### Nile Anderson

lol "hmmm" as in intriguing

13. Jun 3, 2016

### BvU

Ah, posts crossed. Well done. On to the next exercise.

PS
You have a force $F$ to accelerate a mass $m$ from rest with constant acceleration over a distance $d$. What is the final velocity ?​
was meant to seduce you to calculate v as a function of knowns:
$$\ d = {1\over 2} at^2\ \Rightarrow t = \sqrt{2d\over a} \Rightarrow v = at = {F\over m} \sqrt{2dm\over F} \Rightarrow v\propto 1/\sqrt m$$