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Question

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


A
ac^k
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B
2ac2^j
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C
ac2^j
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D
a2c^j
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Solution

The correct option is B $$2ac^{2}\hat{j}$$
Given that:
acceleration along x = 0;
i.e. $$\dfrac{dx}{dt} = c$$
also given that 
$$y = ax^{2}$$
differentiating with time.
$$\dfrac{dy}{dt} = 2ax \dfrac{dx}{dt} = 2acx $$
differentiating again we get $$a=2ac^2$$

Physics

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