Speed of a body moving with uniform acceleration is u . This speed is doubled while covering a dista

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2.Motion in Straight Line

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The speed of a body moving with uniform acceleration is $u$. This speed is doubled while covering a distance $S$. When it covers an additional distance $S$, its speed would become

A

$\sqrt 3 \,u$

B

$\sqrt 5 \,u$

C

$\sqrt {11} \,u$

D

$\sqrt 7 \,u$

Solution

(d) As ${v^2} = {u^2} + 2as$ ==> ${(2u)^2} = {u^2} + 2as \Rightarrow 2as = 3{u^2}$

Now, after covering an additional distance $s$, if velocity becomes $v$, then,

${v^2} = {u^2} + 2a(2s)$$ = {u^2} + 4as$$ = {u^2} + 6{u^2}$$ = 7{u^2}$

$\therefore v = \sqrt 7 u$.

Standard 11

Physics

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