A particle moves in the plane xy with velocity v = a 
+ bx 
, where 
and 
are the unit vectors of the x and y axes and a and b are constants. At the initial moment of time the particle was located at the point x = y = 0. Find:
Text Solution
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The velocity vector of the particle
So, 
…… (1)
From (1) 
… .(2)
And 
Integrating 
or, 
… ..(3)
From Eqs. (2) and (3), we get, 
… .(4)
The curvature radius of trajectory 
is:
…… (5)
Let us differentiate the path Eq. 
with respect to 
,
… ..(6)
From Eqs. (5) and (6), the sought curvature radius :
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