Understanding the Problem:
We are given a particle moving in one dimension under the action of a constant force. The distance x of the particle is related to time t by the equation t = √(x^3), where x is in meters and t is in seconds. We need to find the displacement when the velocity of the particle is zero.

Understanding the Equation:
The given equation t = √(x^3) represents the relationship between the distance x and time t. It indicates that the time taken by the particle to cover a certain distance x is equal to the square root of that distance cubed.

Finding the Velocity:
To find the displacement when the velocity is zero, we need to first find the velocity as a function of time. Since velocity is the derivative of displacement with respect to time, we can differentiate the given equation with respect to t to find the velocity function.

Differentiating both sides of the equation t = √(x^3) with respect to t:
d/dt(t) = d/dt(√(x^3))
1 = (3/2) * x^(3/2) * dx/dt

Simplifying the equation, we get:
dx/dt = 2/3 * (1 / x^(3/2))

Finding the Displacement:
To find the displacement when the velocity is zero, we need to determine the value of x when dx/dt = 0. Setting dx/dt equal to zero and solving for x:
0 = 2/3 * (1 / x^(3/2))

Multiplying both sides by 3/2 and taking the reciprocal:
0 = 1 / (x^(3/2))
0 = x^(3/2)

Since x^(3/2) = 0, we can conclude that x = 0.

Therefore, when the velocity of the particle is zero, the displacement (x) is also zero. This implies that the particle is at the origin, or its initial position.

Summary:
- The distance x of a particle moving in one dimension under the action of a constant force is related to time t by the equation t = √(x^3).
- The velocity of the particle can be found by differentiating the equation with respect to time.
- To find the displacement when the velocity is zero, we set the derivative of x with respect to t equal to zero and solve for x.
- The solution x = 0 indicates that the particle is at the origin or its initial position when the velocity is zero.

Here first of all square root of x is defined only when x is greater than or equal to zero. Now then t must be greater than or equal to 3 second. We differentiate x w.r.t. to time then we observe that at t equal to 3 second , velocity becomes zero. And if the time less than 3 second ofcourse velocity is defined but square root of x is not defined .And hence we take motion starts from t is equal to 3 second and it is at x equal to zero and hence displacement is zero when particle is at rest momentarily.