31. The displacement ’ x ’ (in meter) of a particle of mass ’ m ’ (in kg ) moving in one dimension under the action of a force, is related to time ’ t ’ (in sec) by t = √x+ 3. The displacement of the particle when its velocity is zero, will be

31. The displacement ’ x ’ (in meter) of a particle of mass ’ m ’ (in kg ) moving in one dimension under the action of a force, is related to time ’ t ’ (in sec) by t =  √x+ 3. The displacement of the particle when its velocity is zero, will be

(a) 2 m

(b) 4 m

(c) 0 m

(d) 6 m

Answer :  (c) 0 m

\( t = \sqrt{x} + 3 \)

\( \rightarrow t - 3 = \sqrt{x} \)

\( \rightarrow x = (t - 3)^2 \)

\( v = \)\(\frac{dx}{dt}\)\( = 2(t - 3) \)

\( 2(t - 3) = 0 \)

\( \rightarrow t = 3 \, \text{s} \)

\( x_{t=3} = 0 \, \text{m} \)