An athlete runs a distance of 1500 m in the following manner (1) starting from rest he accelerates himself at 2m/s^2 , till he covers a distance of 900 m (2) He then runs the remaining distance of 600 m at the uniform speed developed. C alculate the time taken by the athlete to cover the two parts of the distance travelled. Also find the time when he is at the center of the track.

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Solution

Dear Student ,
$1500 m r a c e s a r e r u n o n o v a l t r a c k s, n o t s t r a i g h t l i n e t r a c k s . R u n n e r s d o n o t m o v e t o w a r d t h e " c e n t e r o f t h e t r a c k " . P e r h a p s t h e y w a n t t h e t i m e w h e n t h e d i s \tan c e c o v e r e d i s 750 m . T h e s p e e d r e a c h e d d u r i n g t h e f i r s t p a r t w o u l d b e, V = \sqrt{2 a X} = 60 m / s I t w o u l d t a k e h i m \frac{V}{a} = 30 s t o r e a c h t h a t s p e e d . T h e l a s t 600 m w o u l d b e r u n i n 600 / 60 = 10 s . N o o n e c a n r u n t h a t f a s t . A c h a m p i o n d i s \tan c e r u n n e r w i l l r e a c h a p e a k s p e e d o f a b o u t 8 m / s .$
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