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Maths-

General

Easy

Question

A particle moves along a straight line with the law of motion given by $s to the power of 2 end exponent equals a t to the power of 2 end exponent plus 2 b t plus c.$ then the acceleration varies are

$\frac{1}{s^{3}}$
$\frac{1}{s}$
$\frac{1}{s^{4}}$
$\frac{1}{s^{2}}$

The correct answer is: $fraction numerator 1 over denominator s to the power of 3 end exponent end fraction$

Given, s= $square root of a t to the power of 2 end exponent plus 2 b t plus c end root$
$rightwards double arrow blank fraction numerator d s over denominator d t end fraction equals fraction numerator 2 a t plus 2 b over denominator 2 square root of a t to the power of 2 end exponent plus 2 b t plus c end root end fraction equals fraction numerator a t plus b over denominator square root of a t to the power of 2 end exponent plus 2 b t plus c end root end fraction$

$fraction numerator d to the power of 2 end exponent s over denominator d t to the power of 2 end exponent end fraction equals fraction numerator open square brackets fraction numerator table row cell square root of a t to the power of 2 end exponent plus 2 b t plus c plus a end root end cell row cell negative open parentheses a t plus b close parentheses fraction numerator open parentheses 2 a t plus 2 b close parentheses over denominator 2 square root of a t to the power of 2 end exponent plus 2 b t plus c end root end fraction end cell end table over denominator open parentheses square root of a t to the power of 2 end exponent plus 2 b t plus c end root close parentheses to the power of 2 end exponent end fraction close square brackets over denominator open parentheses square root of a t to the power of 2 end exponent plus 2 b t plus c end root close parentheses to the power of 2 end exponent end fraction$

$rightwards double arrow blank fraction numerator d to the power of 2 end exponent over denominator d t to the power of 2 end exponent end fraction equals fraction numerator a c minus b to the power of 2 end exponent over denominator s to the power of 3 end exponent end fraction rightwards double arrow A c c e l e r a t i o n proportional to fraction numerator 1 over denominator s to the power of 3 end exponent end fraction$

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