Max/min Problem (1 Viewer)

[nazfiz]

Heu Guys,
I need help with question b part iii. not too sure on how to do it.
help would be appreciated.
Thanks in advance!

 

[deswa1]

I haven't had a go at the problem but from a 2 second glance, try using distance=speedxtime. Let me know if that works. If it doesn't, I'll try and do the whole problem for you

 

[nazfiz]

I haven't had a go at the problem but from a 2 second glance, try using distance=speedxtime. Let me know if that works. If it doesn't, I'll try and do the whole problem for you

I used my value from part ii for velocity and multiplied it with the time i got in part ii as well.
v=1.08
t=3
d=3.24km
But in the answers it says d=4.32. that's the problem

 

[deswa1]

Allright, I'll have a go after dinner

 

[bleakarcher]

v=0.12t(6-t)=dx/dt
Integrating with respect to time:
=>x=0.12[3t^2-0.5t^2]+C
When t=0, x=0 (note x describes the displacement (or in this case, distance) from the first station after a time t):
C=0
Hence, x=0.12[3t^2-(1/3)t^3]
From part (i) we know that when t=6 minutes the train reaches the second station so when t=6:
=>x=0.12[3*6^2-(1/3)*6^3] km

 

[Kimyia]

Like bleakarcher's solution, its not a max/min problem.
You integrate velocity to get your displacement formula.
Find out when the train is at rest by making velocity = 0. And you end up with t=0 and t=6.
So you know at t=0, your displacement is going to be 0. Then at t=6, when the train reaches the other station, displacement = 4.32. So if the train's travelled from 0 to 4.32, then the distance is 4.32.

 

[nazfiz]

v=0.12t(6-t)=dx/dt
Integrating with respect to time:
=>x=0.12[3t^2-0.5t^2]+C
When t=0, x=0 (note x describes the displacement (or in this case, distance) from the first station after a time t):
C=0
Hence, x=0.12[3t^2-(1/3)t^3]
From part (i) we know that when t=6 minutes the train reaches the second station so when t=6:
=>x=0.12[3*6^2-(1/3)*6^3] km

Thank you so much! That completely slipped my mind.

 

[bleakarcher]

with maths, always have an open mind.

 

[nazfiz]

Allright, I'll have a go after dinner

Thanks Delsa, but you don't have to do it.