**Position of the Particle when Acceleration becomes 30 m/s^2**

To determine the position of the particle when the acceleration becomes 30 m/s^2, we need to integrate the given velocity function with respect to time.

The velocity function is given as v = x^2 * x, where x is in meters and v is in meters per second. To integrate this function, we need to express the velocity as a function of time.

Since velocity (v) is the rate of change of position (x) with respect to time (t), we can rewrite the velocity function as v = dx/dt.

**Integrating the Velocity Function**

To integrate the velocity function, we can rewrite it as:
dx/dt = x^2 * x

Separating variables, we get:
dx/x^2 = x dt

Integrating both sides, we have:
∫(1/x^2) dx = ∫x dt

This gives us:
-1/x = (1/2)x^2 + C

Simplifying the equation, we get:
x = -1 / [(1/2)x^2 + C]

**Determining the Constant of Integration**

To determine the constant of integration (C), we need additional information. Since the problem statement doesn't provide any initial conditions or constraints, we cannot determine the exact value of C. Therefore, we'll consider it as an arbitrary constant.

**Finding the Position when Acceleration is 30 m/s^2**

To find the position of the particle when the acceleration becomes 30 m/s^2, we need to differentiate the velocity function with respect to time to obtain the acceleration function.

Differentiating the velocity function, we have:
a = dv/dt = d/dt(x^2 * x)

Simplifying, we get:
a = 2x * dx/dt + x^2

Substituting dx/dt = x^2 * x, we get:
a = 2x * (x^2 * x) + x^2
a = 2x^4 + x^2

Now, we can set the acceleration function equal to 30 m/s^2 and solve for x:
2x^4 + x^2 = 30

This equation is a quartic equation, which may have multiple solutions. Solving it will provide the different positions of the particle when the acceleration is 30 m/s^2.

Note: The solution to the quartic equation may require the use of numerical methods or approximation techniques if a symbolic solution cannot be obtained.

In conclusion, to determine the position of the particle when the acceleration becomes 30 m/s^2, we need to integrate the given velocity function and solve the resulting equation. However, without additional information or constraints, we cannot determine the exact position.

dx/dt=x^2+xhence dv/dt=2x+1given that acceleration is 30 m/s^2.so ,30=2x+1x=14.5