The displacement ' $x$ ' (in meter) of a particle of mass ' $m$ ' (in kg) moving in one dimension under the…

The displacement ' $x$ ' (in meter) of a particle of mass ' $m$ ' (in kg) moving in one dimension under the action of a force, is related to time ' $t$ ' (in sec) by $t=\sqrt{x}+3$. The displacement of the particle when its velocity is zero, will be
  1. $2 \mathrm{~m}$
  2. $4 \mathrm{~m}$
  3. zero
  4. $6 \mathrm{~m}$

Solution

$\begin{aligned} & \because t=\sqrt{x}+3 \\ & \Rightarrow \sqrt{x}=t-3 \Rightarrow x=(t-3)^{2} \\ & v=\frac{d x}{d t}=2(t-3)=0 \\ & \Rightarrow t=3 \\ & \therefore x=(3-3)^{2} \\ & \Rightarrow x=0 \end{aligned}$

Asked in: JEE Mains - Motion In One Dimension - Test 3

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