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Introduction

A particle mo...

Question

A particle moves according to the equation $x = 2 t^{2} - 5 t + 6$ . The average velocity in the first $3 s$ and velocity at $t = 3 s$ are repectively.

1 m s^{- 1}, 7 m s^{- 1}

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4 m s^{- 1}, 3 m s^{- 1}

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2 m s^{- 1}, 5 m s^{- 1}

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3 m s^{- 1}, 7 m s^{- 1}

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Solution

The correct option is A $1 m s^{- 1}, 7 m s^{- 1}$
$x = 2 t^{2} - 5 t + 6 \Rightarrow v = \frac{d x}{d t} = 4 t - 5 \Rightarrow v = 7 m s^{- 1} a t t = 3 s e c o n d s . N o w, P o s i t i o n i n t = 3 s e c o n d s \Rightarrow x = 18 - 15 + 6 = 9 m e t e r s . a n d p o s i t i o n a t t = 0 s e c o n d s i s 6 m \Rightarrow A v e r a g e v e l o c i t y = \frac{9 - 6}{3} = 1 m s^{- 1}$

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