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Relative Velocity

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Question

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5. A particle at rest starts with acceleration 5 m/s² on a straight line for 4 s. The it decelerates at 2.5 m/s² to rest. Average velocity during the journey is.

(1) 20 m/s (2) 10 m/s

(3) 5 m/s (4) 15 m/s

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Solution

Dear Student

$a b o d y i s m o v i n g f o r 4 s e c w i t h a c c e l e r a t i o n 5 m s^{- 2} I n v - t g r a p h, s l o p e = \frac{m a x i m u m v e l o c i t y}{t i m e t a k e n} 5 = \frac{v_{m a x}}{4} v_{m a x} = 20 m s^{- 1} I n n e x t h a l p 2.5 = \frac{20}{t'} t' = 8 s e c T o t a l t i m e = 8 + 4 = 12 s e c t o t a l d i s \tan c e = 1 / 2 \times 12 \times 20 = 120 m A v e r a g e v e l o c i t y = \frac{t o t a l d i s \tan c e}{t o t a l t i m e} = 120 / 12 = 10 m s^{- 1} R e g a r d s$

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