PYQ NEET- Motion In A Straight Line Kinematics L-7

Question: The displacement ’ $x$ ’ (in meter) of a particle of mass ’ $\mathrm{m}$ ’ (in $\mathrm{kg}$ ) 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#

A) $4 \mathrm{~m}$

B) $0 \mathrm{~m}$ (zero)

C) $6 \mathrm{~m}$

D) $2 \mathrm{~m}$

Answer: $0 \mathrm{~m}$ (zero)#

Sol:#

As $\mathrm{t}=\sqrt{x}+3$ $$ \begin{aligned} & \Rightarrow \sqrt{x}=t-3 \ & \Rightarrow x=(t-3)^2 \end{aligned} $$

Velocity, $\mathrm{v}=\frac{d x}{d t}=2(t-3)$

Velocity of the particle becomes zero, when $$ 2(t-3)=0 \Rightarrow \mathrm{t}=3 \mathrm{~s} $$

At $t=3 s$, $$ x=(3-3)^2=0 \mathrm{~m} $$