A sprinter in a 100 m race covers 4m in first second, 30 m in next 4 seconds and 52 m in another 4 s and finishes the race in 10 seconds. (1) Calculate the average speed of the sprinter? (2) What is the peak value attained by the sprinter? (3) During which time interval is the acceleration highest?(4) Plot the distance and velocity time graph for the race? (5) Show on the graph the velocity of sprinter at the end of 5 seconds?

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Solution

Dear student,
$1) V a g = \frac{t o t a l d i s \tan c e}{t o t a l t i m e t a k e n} = \frac{100 m}{1 + 4 + 4 + 10} = 5.263 m / s 2) P e a k s p e e d = 50 m e t e r s i n 5 s e c o n d = 12.5 m / s 4 m i n 1 s e c o n d = 4 m / s 30 m e t e r s i n 4 s e c o n d = 30 / 4 = 7.5 m / s 50 m i n 4 s e c o n d = 12.5 16 m i n 10 s = 1.6 m / s 3) a c c e l e r a t i o n f i r s t 1 s = \frac{4 - 0}{1} = 4 m / s^{2} A c c e l e r a t i o n \frac{7.5 - 4}{4 - 1} = \frac{3.5}{3} = 1.16 m / s^{2} A c c e l e r a t i o n \frac{12.5 - 7.5}{9 - 5} = 1.25 m / s^{2} A c c e l e r a t i o n \frac{1.6 - 12.5}{19 - 9} = \frac{- 10.9}{10} = - 1.09 m / s^{2} A c c e l e r a t i o n i s m a x i m u m i n f i r s t s e c o n d .$
Regards

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