Question

the relation 3t=√3√x+6 describes the position of a particle in one direction were x is in metres and t is in sec . The displacement, when velocity is zero,is

Answer 1

differentiate on both sides with respect to time then. 3=(√3v/2√x). 6√x=√3v. when v=0, x=0

Answer 2

It is not clear where it is:  √x  + 6  or   √(x+6) ??

case 1)

3 t = √3 √x  + 6 
x  =  3 (t - 2)² 

v = dx/dt = 6 t - 12
v = 0  when  t = 2 sec.

x = 3 (2-2)² = 0  meters.

case 2)

    3 t = √3  √(x+6)
    x = 3 t² - 6
    v = dx/dt = 6 t
    So velocity = 0  when t = 0.
    displacement x at t  = 0 :   x = - 6 meters.