A particle starts at the origin and moves along the $x$-axis in such a way that its velocity at the point $(x,0)$ is given by the formula $\frac{dx}{dt} = \cos^{2}{\pi x}$. Then, the particle never reaches the point on

Question

Dr. Abubacker · Accepted Answer

(c)
Given, $\frac{dx}{dt} = \cos^{2}{\pi x}$
On differentiating $w.r.t.x$, we get
$\frac{d^{2}x}{dt^{2}} = - 2\pi\sin{2\pi x =}$ negative
The particle never reaches the point, it means
$\frac{d^{2}x}{dt^{2}} = 0\  \Rightarrow \  - 2\pi\sin{2\pi x =}0$
$\Rightarrow \sin{2\pi x = \sin\pi}$
$\Rightarrow 2\pi x = \pi\  \Rightarrow x = \frac{1}{2}\$
The particle never reaches at $x = \frac{1}{2}$

Q. A particle starts at the origin and moves along the $x$-axis in such a way that its velocity at the point $(x,0)$ is given by the formula $\frac{dx}{dt} = \cos^{2}{\pi x}$. Then, the particle never reaches the point on

Explanation

Reviewed by Dr. Abubacker

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