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V-t to a-t Graph

For a particl...

Question

For a particle in S.H.M. the amplitude and maximum velocity are A and $v$ respectively. Then its maximum acceleration is :

A

v^{2}

/2A

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B

v^{2}

A

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C

v^{2}

/A

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D

v

/A.

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Solution

The correct option is D $v^{2}$ /A
$x = A s i n ω t$
$v = A ω c o s ω t$
$a = - A ω^{2} s i n ω t$
So, as given in problem
$A = A$
$A ω = v$
so, $A ω^{2} = \frac{A ω (A ω)}{A} = \frac{v . v}{A} = \frac{v^{2}}{A}$

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