Question

The displacement x of a particle moving in one dimension is related to time t by the equation $t=\sqrt{x}+3$ where x is in metres and t in seconds. The displacement of the particle when its velocity is zero is

• A. zero
• B. 4 m
• C. 1 m
• D. 0.5 m

Answer 1

The correct option is A

zero

Given that, $t=\sqrt{x}+3$
$\Rightarrow \sqrt{x}=t-3$
Squaring both sides, $x=t^2-6t+9$
Velocity, $v=\frac{dx}{dt}=2t-6$
For velocity, v to be equal to zero, $2t-6=0\Rightarrow t=3s$
At t = 3 s, displacement, $x=t^2-6t+9=3^2-6\times 3+9=0$
Hence, the correct option is (a).