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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 $\frac{d x}{d t}=\cos ^2 \pi x$.
Then the particle never reaches the point on
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Then the particle never reaches the point on
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Verified Answer
The correct answer is:
$x=\frac{1}{2}$
Given $\frac{d x}{d t}=\cos ^2 \pi x$. Differentiate w.r.t. t,
$\begin{aligned} & \frac{d^2 x}{d t^2}=-2 \pi \sin 2 \pi x=-v e \\ & 8 \frac{d^2 x}{d t^2}=0 \Rightarrow-2 \pi \sin 2 \pi x=0 \Rightarrow \sin 2 \pi x=\sin \pi \\ & \Rightarrow 2 \pi x=\pi \Rightarrow x=1 / 2\end{aligned}$
$\begin{aligned} & \frac{d^2 x}{d t^2}=-2 \pi \sin 2 \pi x=-v e \\ & 8 \frac{d^2 x}{d t^2}=0 \Rightarrow-2 \pi \sin 2 \pi x=0 \Rightarrow \sin 2 \pi x=\sin \pi \\ & \Rightarrow 2 \pi x=\pi \Rightarrow x=1 / 2\end{aligned}$
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