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 (d x/d t)= cos 2 π x. Then the particle never reaches the point on

Question

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 (d x/d t)= cos 2 π x. Then the particle never reaches the point on (A) x=(1/4) (B) x=(3/4) (C) x=(1/2) (D) x=1

Tardigrade Admin · Accepted Answer

Given: (d x/d t)= cos 2 π x. Differentiate with respect to t, (d2 x/d t2)=-2 π sin 2 π x=- ve ∵ (d2 x/d t2)=0 ⇒ 2 π sin 2 π x=0 ⇒ sin 2 π x= sin π ⇒ 2 π x=π ⇒ x=(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 $\frac{d x}{d t} = cos^{2} π x$ . Then the particle never reaches the point on

$x = \frac{1}{4}$

$x = \frac{3}{4}$

$x = \frac{1}{2}$

$x = 1$

Given: $\frac{d x}{d t} = cos^{2} π x$ . Differentiate with respect to $t$ ,
$\frac{d ^{2} x}{d t ^{2}} = - 2 π sin 2 π x = - v e$
$∵ \frac{d ^{2} x}{d t ^{2}} = 0$
$\Rightarrow 2 π sin 2 π x = 0$
$\Rightarrow sin 2 π x = sin π$
$\Rightarrow 2 π x = π \Rightarrow x = \frac{1}{2}$

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 dtdx​=cos2πx. Then the particle never reaches the point on

x=41​

x=43​

x=21​

x=1