A radius vector of a particle varies with time t as r-at1- t- where a is a constant vector and - is a positive constant- Find the time interval - t taken by the particle to return to the initial points-

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Standard XII

Physics

1st Equation of Motion

A radius vect...

Question

A radius vector of a particle varies with time $t$ as $r = a t (1 - α t)$ , where $a$ is a constant vector and $α$ is a positive constant. Find the time interval $Δ t$ taken by the particle to return to the initial points.

Δ t = \frac{3}{α}

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Δ t = \frac{1}{2 α}

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Δ t = \frac{2}{α}

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Δ t = \frac{1}{α}

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Solution

The correct option is D $Δ t = \frac{1}{α}$
Put $t = 0$ $⟹ r = 0$ is the initial position in the given equation
$r = a t (1 - α t) = 0 \Rightarrow t = 0 o r t = \frac{1}{α}$

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A radius vector of a particle varies with time t as r=at(1−αt), where a is a constant vector and α is a positive constant. Find the time interval Δt taken by the particle to return to the initial points.

The correct option is D Δt=1αPut t=0 ⟹r=0 is the initial position in the given equationr=at(1−αt)=0⇒t=0ort=1α

A radius vector of a particle varies with time $t$ as $r = a t (1 - α t)$ , where $a$ is a constant vector and $α$ is a positive constant. Find the time interval $Δ t$ taken by the particle to return to the initial points.

The correct option is D $Δ t = \frac{1}{α}$
Put $t = 0$ $⟹ r = 0$ is the initial position in the given equation
$r = a t (1 - α t) = 0 \Rightarrow t = 0 o r t = \frac{1}{α}$