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A-level Futher Mathematics Help....Mechanics

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amina hasan:
I am writing to you with regard to my Edexcel A-level Further Mathematics mechanics modules.The modules that I have chosen are M2,M3,M4,S2,FP1,FP2.  I really need help with the mechanics modules M3 and M4 .I currently reside in Dubai, UAE and am doing Further Mathematics privately (self-studying) since no school in Dubai offers Futher Mathematics. I have managed so far on my own with the help of notebooks of previous students who have already done these modules.Unfortunately nobody has actually done mechanics 3 and 4 so I have no tutor and no notebooks to rely on. I am finding the Mechanics modules very tedious and  have very little time to cover them. I have already done S2,FP1, FP2. Last year I completed the A-levels Mathematics and Pure Mathematics and so this was the only easiest combination of modules for Further Mathematics available to me. Is there any help that you can offer me online , like answering some of my questions or would you know of anybody in Dubai who could be of any help?..

astarmathsandphysics:
I am your man. Post your questions.

amina hasan:
Hey..
Could you help me with this question.(Mechanics 3)-
1.A particle P moves in a straight line with acceleration,at time t seconds, proportional to (t+to)^-3, where t0 is positive and constant. The intial speed of P at t=0 is um/s.Show that the speed of P approches a limiting value as t tends to infinity. Given that this limiting value is 2um/s, show that at time t seconds the particle will have travelled a distance
ut(2t+to)/(t+to) metres.

astarmathsandphysics:

--- Quote from: amina hasan on February 14, 2009, 02:56:44 pm ---Hey..
Could you help me with this question.(Mechanics 3)-
1.A particle P moves in a straight line with acceleration,at time t seconds, proportional to (t+to)^-3, where t0 is positive and constant. The intial speed of P at t=0 is um/s.Show that the speed of P approches a limiting value as t tends to infinity. Given that this limiting value is 2um/s, show that at time t seconds the particle will have travelled a distance
ut(2t+to)/(t+to) metres.

--- End quote ---

dv/dt=k(t+to)^-3

We have to integrate. Add 1 to power and divide by new power. v=(k(t+to)^-2)/-2+c

Thent=0 v=u so u=(k(0+to)^-2)/-2+c=-k/(2(to)^2)+c so c=u+ k/(2(to)^2)

v=k((t+to)^-2)/-2+u+ k/(2(to)^2)=0.5k(((to)^-2)-(t+to)^-2))+u
As t tends to infinity second term in brackets tends to zero so v tends to 0.5k((to)^-2)+u we solve 2u=0.5k((to)^-2)+u so k=2to^2

dx/dt=1/2*2uto^2(-1/(t+to)^2+1/to^2)+u
       
        =u-to^2/(t+to)62+u= 2u-uto^2/(t+to)^2

Integrate x=2ut+uto^2/(t+to)+ c

x=0 t= 0 so c=-uto
and x=2ut+uto^2/(t+to)-uto
=u(2t+to^2/(t+to)-t0?
=u/(t+to)(2t^2+2tto-tto-to^2)
=u/(t+to)(2t^2+tto)=ut(2t+t0)/(t+to)

amina hasan:
thanks....alot

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