The displacement of a particle moving along x-axis changes . . .

Question : The displacement of a particle moving along x-axis changes with time as 2√x=3t, then the velocity of the particle is directly proportional to ______

Doubt by Divya

Solution : 

2√x=3t — (1)

SBS

4x=9t²
differentiating both sides wrt time t

4(dx/dt)=9×2t
4v=18t
v=18/4t
v=4.5t

v∝t 

Also 

v=1.5×3t
v= 1.5×2√x [From equation (1)]
v= 3√x

v∝√x

Hence, velocity of the particle is either directly proportional to time (t) or square root of displacement (x).