If the wagon travels 18.75 m, then the work done on the wagon is
(18.75 m) x (the steady force applied to the wagon all the way, in Newtons) .
The unit is Joules .
Answer:
See explanation below.
Explanation:
For this case we atart fom the proportional model given by the following differential equation:
![\frac{dA}{dt}= kA](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D%20kA)
And if we rewrite this expression we got:
![\frac{dA}{A} = k dt](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7BA%7D%20%3D%20k%20dt)
If we integrate both sides we got:
![ln|A| = kt +C](https://tex.z-dn.net/?f=%20ln%7CA%7C%20%3D%20kt%20%2BC)
And using exponential on both sides we got:
![A(t) = e^{kt} e^C = A_o e^{kt}](https://tex.z-dn.net/?f=%20A%28t%29%20%3D%20e%5E%7Bkt%7D%20e%5EC%20%3D%20A_o%20e%5E%7Bkt%7D)
Where
represent the initial amount for the isotope and t the time in years and A the amount remaining.
If we want to apply a model for the half life we know that after some time definfd
the amount remaining is the hal, so if we apply this we got:
![\frac{A_o}{2} = A_o e^{kt_{1/2}}](https://tex.z-dn.net/?f=%20%5Cfrac%7BA_o%7D%7B2%7D%20%3D%20A_o%20e%5E%7Bkt_%7B1%2F2%7D%7D)
We can cancel
and we got:
![\frac{1}{2}= e^{kt_{1/2}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%3D%20e%5E%7Bkt_%7B1%2F2%7D%7D)
If we solve for k we can apply natural log on both sides and we got:
![ln (\frac{1}{2}) = kt_{1/2}](https://tex.z-dn.net/?f=ln%20%28%5Cfrac%7B1%7D%7B2%7D%29%20%3D%20kt_%7B1%2F2%7D)
![k = \frac{ln(1/2)}{t_{1/2}}](https://tex.z-dn.net/?f=%20k%20%3D%20%5Cfrac%7Bln%281%2F2%29%7D%7Bt_%7B1%2F2%7D%7D)
And that would be our proportional constant on this case.
If we replace this value for k int our model we will see that:
![A(t) =A_o e^{ \frac{ln(1/2)}{t_{1/2}} t}](https://tex.z-dn.net/?f=%20A%28t%29%20%3DA_o%20e%5E%7B%20%5Cfrac%7Bln%281%2F2%29%7D%7Bt_%7B1%2F2%7D%7D%20t%7D)
And using properties of logs we can rewrite this like that:
![A(t) = A_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A_o%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bt_%7B1%2F2%7D%7D%7D)
And thats the common formula used for the helf life time.
I think it’s D because I have heard in previous tests that it ruins the landscapes
We need to use differant energy soureces that are renewable. THis is because at the moment most of the enrgy that we use is unrenewable, coal, oil, petrol etc. It takes millions of year to create and is burnt in a matter of minuetes. We need energy that is renewable so we can supply it quickly when we need it because all nonrenewable enrgy's are running out. Only in 1 million years if a fish dies now will it be compatable to turn into fuel. Wind power, solar power, movement energy are all renewable. THis is why it is very important we use those things. Hope this helped :-) Bonnie Year 7