Introduction:
In this problem, we are given that the velocity of a particle is varying with time according to the equation V = (1/3)Kt, where K is a constant and t is the time. We need to determine the acceleration of the particle and explain its relationship with the given equation.

Understanding the problem:
To find the acceleration of the particle, we need to differentiate the velocity equation with respect to time. The resulting expression will give us the acceleration as a function of time. By examining this expression, we can determine the relationship between acceleration and the given equation.

Differentiating the velocity equation:
Let's differentiate the velocity equation V = (1/3)Kt with respect to time t to find the acceleration a.

dV/dt = d/dt((1/3)Kt)

To differentiate (1/3)Kt, we can use the power rule of differentiation, which states that d/dt(x^n) = nx^(n-1), where n is a constant and x is a variable.

dV/dt = (1/3)K * d/dt(t)

Since the derivative of t with respect to t is 1, the equation simplifies to:

dV/dt = (1/3)K * 1

Therefore, the acceleration a is given by:

a = dV/dt = (1/3)K

Relationship between acceleration and the given equation:
From the above expression, we can see that the acceleration is proportional to the constant K. This means that as the value of K changes, the acceleration will also change proportionally. However, the acceleration is independent of time, as it does not contain the variable t in the expression.

Conclusion:
The acceleration of the particle is given by a = (1/3)K, where K is a constant. The acceleration is proportional to the constant K and does not vary with time.