Q.):- A body moving with uniform acceleration covers 100 m in the first 10 seconds and 150 m in the next 10 seconds. What is the initial velocity of the body.

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Solution

Dear student,

$A b o d y i s m o v i n g w i t h i n i t i a l v e l o c i t y u m s^{- 1} a n d a c c e l e r a t i o n a i t m o v e d 100 m i n 10 s e c a n d 150 m i n (10 + 10) = 20 s e c S = u t + \frac{1}{2} a t^{2} F o r 100 m 100 = u \times 10 + \frac{1}{2} \times a \times 10^{2} \Rightarrow 100 = 10 u + 50 a \Rightarrow u + 5 a = 10 - - (1) F o r 150 m i n 20 s e c 150 = u \times 20 + \frac{1}{2} \times a \times 20^{2} \Rightarrow 150 = 20 u + 200 a \Rightarrow 4 u + 40 a = 30 - - (2) s o l v i n g (1) a n d (2) u + 5 a = 10] \times 8 8 u + 40 a = 80 4 u + 40 a = 30 - - - 4 u = 50 \Rightarrow u = \frac{50}{4} \Rightarrow u = \frac{25}{2} \Rightarrow u = 12.5 m / s t h u s t h e i n i t i a l v e l o c i t y i s 12.5 m / s e c$
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