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Standard XII

Physics

Differentiation

A particle mo...

Question

A particle moves along the parabolic path $y = a x^{2}$ in such a way that the x component of the velocity remains constant, say c. The acceleration of the particle is

a c^k

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2 a c^{2}^j

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2 a c^{2}^k

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a^{2} c^j

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Solution

The correct option is B $2 a c^{2}^j$
$y = a x^{2}, \frac{d y}{d t} = a (2 x) \frac{d x}{d t} = 2 a c x, \frac{d^{2} y}{d t^{2}} = 2 a c \frac{d x}{d t} = 2 a c^{2}$

$a_{y} = 2 a c^{2}, a_{x} = 0, \to a = a_{x}^i + a_{y}^j$

$∴ \to a = 2 a c^{2}^j$

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The correct option is B 2ac2^jy=ax2, dydt=a(2x)dxdt=2acx, d2ydt2=2acdxdt=2ac2 ay=2ac2, ax=0, →a=ax^i+ay^j ∴→a=2ac2^j

A particle moves along the parabolic path $y = a x^{2}$ in such a way that the x component of the velocity remains constant, say c. The acceleration of the particle is

The correct option is B $2 a c^{2}^j$
$y = a x^{2}, \frac{d y}{d t} = a (2 x) \frac{d x}{d t} = 2 a c x, \frac{d^{2} y}{d t^{2}} = 2 a c \frac{d x}{d t} = 2 a c^{2}$

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