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April 13th, 2017, 04:02 AM  #1 
Newbie Joined: Apr 2017 From: India Posts: 17 Thanks: 0  Differential equations
While deriving the equation for transverse acceleration, I came across following problem: It is written that: transverse acceleration=(dr/dt)*(ds/dt)+(dr/dt)*(ds/dt)+ r(d^2(s)/dt^2) In the next step it is written that this is equal to: Transverse acceleration = 1/r {(r^2)(d^2 (s))/(dt^2) +2r(ds/dt)}.......How?? 
April 13th, 2017, 04:45 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,570 Thanks: 613 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
April 13th, 2017, 07:27 AM  #3 
Newbie Joined: Apr 2017 From: India Posts: 17 Thanks: 0 
Well, yes I have the same doubt and after that they have written that: Transverse acceleration= 1/r {d((r^2)ds/dt)/dt} 
April 13th, 2017, 08:41 AM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,570 Thanks: 613 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
April 13th, 2017, 05:25 PM  #5 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,320 Thanks: 450 Math Focus: Yet to find out. 
transverse acceleration $= \dfrac{dr}{dt}*\dfrac{ds}{dt} + \dfrac{dr}{dt}*\dfrac{ds}{dt} + r \dfrac{d^2(s)}{dt^2}$ Transverse acceleration = $\dfrac{1}{r} * \dfrac{(r^2) (d^2 (s))}{dt^2} +2r \dfrac{ds}{dt}$ Transverse acceleration= $\dfrac{1}{r} \dfrac{\dfrac{d((r^2)ds}{dt}}{dt}$ This is the exact sequence of steps provided in your text? 

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