# M2 help - again

Discussion in 'Mathematics' started by Maths_Mike, Aug 14, 2011.

1. ### Maths_MikeNew commenter

Ok - i know i need to differentiate to get the velocity and then set it to 0 - but I cant seen to get it to work.
s=1/k(g/k +U)(1-e^-kt)-gt/k where k and U are constants. Model valid while particle moving upwards.
Show valid while 0<=t<= 1/k ln(1+kU/g)

2. ### Maths_MikeNew commenter

Ok - i know i need to differentiate to get the velocity and then set it to 0 - but I cant seen to get it to work.
s=1/k(g/k +U)(1-e^-kt)-gt/k where k and U are constants. Model valid while particle moving upwards.
Show valid while 0<=t<= 1/k ln(1+kU/g)

3. ### DMNew commenter

Can you put some brackets in to make it clear which bits are on the top or bottom of the fraction?

4. ### Maths_MikeNew commenter

(1/k)(g/k +U)(1-e^-kt)-(gt/k)
(1/k)ln(1+kU/g)

5. ### DMNew commenter

Your method works. What did you get for v?

6. ### DMNew commenter

Got fed up pressing refresh.
You should have obtained:
v = exp(-kt) ((g/k) + U) - (g/k)

7. ### Maths_MikeNew commenter

crumbs sry for the not very quick reply!

9. ### Maths_MikeNew commenter

anyway it seems i made a mistake with my differentiating!

Ok.

11. ### Maths_MikeNew commenter

on hang on - i just didnt cancel the 1/k with the (ke^-kt)

12. ### Maths_MikeNew commenter

may still need some more help!

13. ### DMNew commenter

On this or something else?

14. ### Maths_MikeNew commenter

this.
i have got e^-kt = (gk/g+kU)
but still stuck!

15. ### DMNew commenter

You should have e^(-kt) = g/(g + kU) so an extra k has crept in.

16. ### Maths_MikeNew commenter

just got it! thanks again!

17. ### DMNew commenter

I did:

g/k = (g/k + U) exp(-kt)

g/k = ((g + kU)/k) exp(-kt)

exp(kt) = (g + kU)/g

18. ### Maths_MikeNew commenter

I am ok to say that if e^-kt = 1+(g/kU) then e^kt = 1+(kU/g) -- i.e sort of doing the reciprocal of both sides - or is there a better way of explaining this?

19. ### Maths_MikeNew commenter

Ok just got your last post so all clear - thanks

20. ### DMNew commenter

That looks like you are saying if x = a + b then 1/x = 1/a + 1/b.