**Uniform acceleration**

When the displacement of an object is proportional to the square of time, it implies that the object is experiencing uniform acceleration. This can be explained using the following points:

1. **Displacement and time relationship:** The statement "displacement is proportional to the square of time" means that the displacement of the object (denoted by 's') is directly proportional to the square of time (denoted by 't^2'). Mathematically, this can be represented as s ∝ t^2.

2. **Proportional relationship:** The proportionality sign (∝) indicates that there is a constant of proportionality involved in the relationship. Let's assume this constant to be 'k'. Therefore, the relationship can be written as s = k * t^2.

3. **Acceleration and displacement relationship:** In physics, acceleration (denoted by 'a') is defined as the rate of change of velocity with respect to time. Since velocity is the rate of change of displacement with respect to time, we can derive the relationship between acceleration and displacement as a = (d^2s)/(dt^2), where (d^2s) represents the second derivative of displacement with respect to time.

4. **Deriving the acceleration equation:** To find the acceleration equation, we need to differentiate the displacement equation with respect to time twice. Differentiating s = k * t^2 once with respect to time yields ds/dt = 2k * t. Differentiating it again gives d^2s/dt^2 = 2k, which is a constant value.

5. **Interpreting the constant acceleration:** The fact that the second derivative of displacement with respect to time is a constant value (2k) indicates that the object is experiencing uniform acceleration. Uniform acceleration means that the object's velocity is changing at a constant rate over time.

Therefore, based on the given information that the displacement of an object is proportional to the square of time, we can conclude that the object moves with uniform acceleration.