Question

The relation 3t=√(3x) +6 describes the displacement of the particle in one direction where x is in meter and t is in seconds. The displacement, when velocity is zero

Answer 1

the relation is $3t=\sqrt{3x}+6$ describes the displacement of particle in one direction where x is in metre and t is in second.
we have to find displacement when velocity is zero. e.g., dx/dt = 0

$\text{now,}3t=\sqrt{3x}+6\\\\3t-6=\sqrt{3x}\\\\(3t-6)^2=3x\\\\x=\frac{1}{3}(9t^2-36t+36)\\\\\text{differentiate with respect to t}\\\\\frac{dx}{dt}=\frac{1}{3}(18t-36)=0\\\\t=2$

hence, displacement at t = 2
x = 0

Answer 2

at t=3 and t= 2 we get displacement x= 0 so answer is zero