A particle moves along an arc of radius R its velocity is V depends on the distance X by the relation V = a where a is a constant the tan0 where 0 is the angle between total accelaration and Tangential Accelaration what is tan0 =

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Solution

$L e t u s c o n s i d e r, \tan g e n t i a l a c c e l e r a t i o n = a a n d t r a n s v e r s e a c c e l e r a t i o n = α . T o t a l a c c e l e r a t i o n = \sqrt{(a^{2} + α^{2})} = \sqrt{(a^{2} + \frac{a^{2}}{R^{2}})} B e c a u s e a = α \times R w h e r e R i s t h e r a d i u s o f t h e a r c . t h i s t o t a l a c c e l e r a t i o n m a k e s a n a n g l e θ w i t h d i r e c t i o n o f \tan g e n t i a l a c c e l e r a t i o n . T h e r e f o r e \tan θ = \frac{a}{\sqrt{(a^{2} + \frac{a^{2}}{R^{2}})}} o r \tan θ = \frac{R}{\sqrt{(1 + R^{2})}}$

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