a particle has a magnitude of u towards east at t=0 .its acceleration is towards west and is const. let X_aand X_{b be the magnitude of the displacements in first 10 sec. and the next 10 sec. then}
X_ab
X a=Xb
X_aX_b
_{data is insufficient}

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Solution

$l e t t h e a c c e l e r a t i o n b e a . S i n c e i t i s a c t i n g i n a d i r e c t i o n o p p o s i t e t o t h e m o t i o n o f t h e p a r t i c l e t h e r e f o r e i t i s c o n v i n i e n t t o t a k e i t a s - a n o w, f r o m s e c o n d e q u a t i o n o f m o t i o n : X_{a} = u \times 10 + \frac{1}{2} \times (- a) \times 10^{2} X_{a} = 10 u - 50 a - - - - - - - (1) n o w, v e l o c i t y o f t h e p a r t i c l e a f t e r t h e f i r s t 10 s e c o n d s f r o m f i r s t e q u a t i o n o f m o t i o n : v = u + a t v = u - 10 a t h i s v e l o c i t y w i l l a c t a s t h e i n i t i a l v e l o c i t y o f t h e p a r t i c l e f o r t h e n e x t 10 s e c o n d s n o w, f r o m s e c o n d e q u a t i o n o f m o t i o n : X_{b} = (u - 10 a) \times 10 + \frac{1}{2} (- a) \times 10^{2} X_{b} = 10 u - 100 a - 50 a X_{b} = 10 u - 150 a - - - - - (2) c o m p a r i n g e q u a t i o n (1) a n d e q u a t i o n (2), X_{a} > X_{b}$

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