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Physics-

General

Easy

Question

A particle moves along a parabolic path $y equals 9 x to the power of 2 end exponent$ in such a way that the $x$ -component of velocity remains constant and has a value $fraction numerator 1 over denominator blank 3 end fraction m s to the power of negative 1 end exponent$ . The acceleration of the particle is

$\frac{1}{3} \hat{j} m s^{- 2}$
3 $\hat{j} m s^{- 2}$
$\frac{2}{3} \hat{j} m s^{- 2}$
2 $\hat{j} m s^{- 2}$

The correct answer is: 2 $stack j with hat on top m s to the power of negative 2 end exponent$

$x equals 30 plus 180 equals$ 120m
$y equals 9 x to the power of 2 end exponent$
$rightwards double arrow blank fraction numerator d y over denominator d t end fraction equals v subscript y end subscript equals 18 x fraction numerator d x over denominator d t end fraction equals 18 x open parentheses fraction numerator 1 over denominator 3 end fraction close parentheses$
$rightwards double arrow blank fraction numerator d y over denominator d t end fraction equals v subscript y end subscript equals 6 x$
$a subscript y end subscript equals fraction numerator d to the power of 2 end exponent y over denominator d t to the power of 2 end exponent end fraction equals fraction numerator d v subscript y end subscript over denominator d t end fraction equals 6 open parentheses fraction numerator d x over denominator d t end fraction close parentheses equals 6 open parentheses fraction numerator 1 over denominator 3 end fraction close parentheses$
$rightwards double arrow blank a subscript y end subscript equals 2 m s to the power of negative 2 end exponent$ along $y$ -axis.
Hence, $a subscript y end subscript equals open parentheses 2 m s to the power of negative 2 end exponent close parentheses stack j with hat on top$

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