Question

The displacement x of a particle moving in one dimension under constant acceleration is related to the time t as $t=\sqrt{x}+3$. The displacement of the particle when its velocity is zero is

• A. zero
• B. 3 units
• C. $\sqrt{3}$ units
• D. 9 units

Answer 1

Answer: (A)

zero

$\begin{array}{c}t=\sqrt{x}+3\\ 1=\frac{1}{2\sqrt{x}}.\left(\frac{dx}{dt}\right)\\ \Rightarrow \frac{dx}{dt}=2\sqrt{x}\\ atv=0\\ \frac{dx}{dt}=0\\ \Rightarrow 2\sqrt{x}=0\\ \Rightarrow t-3=0\\ \Rightarrow t=3\\ \therefore \sqrt{x}=t-3=0\end{array}$

displacement =0

$\therefore$ Option $A$ is correct.