Question

a particle is in motion along x-axis such that its acceleration is propotional to x^(2/3).Then the power of the resultant force acting on it is proportional to time t raised to the power?

Answer 1

kindly show the steps involved in getting the answer

Answer 2

This one's actually pretty interesting. Which class is this for?

Answer 3

11th i assumed real values for (some numbers )for this question and was close to the answer but i want to know how it is done logically

Answer 4

Anyways, my solution to the problem: We are given that
\[ \frac{d^2 x}{dt^2} = \alpha x^{\frac{2}{3}} \]
where alpha is some constant. Behold some trickery:
\[\frac{d}{dt} = \frac{dx}{dt} \frac{d}{dx} \]
so we can write the acceleration as
\[ \frac{d^2 x}{dt^2} = \frac{d}{dt} \frac{dx}{dt} = \frac{dx}{dt} \frac{d}{dx} \frac{dx}{dt} = \frac{1}{2} \frac{d}{dx} \left(\frac{dx}{dt}\right)^2\]

Answer 5

Before I keep going on this.... is that a direct quote of the question? I want to make sure you mean to use the word power rather than magnitude.

Answer 6

this is wat is given in the problem i dont know whether they r asking for