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Maths-

General

Easy

Question

If a particle moving along a line follows the law $t equals a s to the power of 2 end exponent plus b s plus c$ , then the retardation of the particle is proportional to

Square of the velocity
Cube of the displacement
Cube of the velocity
Square of the displacement

The correct answer is: Cube of the velocity

We have,
$t equals a s to the power of 2 end exponent plus b s plus c$

$rightwards double arrow 1 equals open parentheses 2 a s plus b close parentheses fraction numerator d s over denominator d t end fraction$

$rightwards double arrow fraction numerator d s over denominator d t end fraction equals fraction numerator 1 over denominator 2 a s plus b end fraction rightwards double arrow fraction numerator d to the power of 2 end exponent s over denominator d t to the power of 2 end exponent end fraction equals negative fraction numerator 2 a over denominator open parentheses 2 a s plus b close parentheses to the power of 2 end exponent end fraction fraction numerator d s over denominator d t end fraction equals negative 2 a open parentheses fraction numerator d s over denominator d t end fraction close parentheses to the power of 3 end exponent$

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