Option 1 states that the distance an object covers in a certain interval of time depends on its initial velocity. This means that the initial velocity of the object affects the distance it will travel during that time period.

Option 2 states that the distance covered is independent of the object`s initial velocity. However, this is incorrect because the initial velocity does play a role in determining the distance traveled. The object`s initial velocity affects how quickly it accelerates and therefore influences the distance covered.

Option 3 states that the distance covered increases linearly with time. This is not necessarily true for an object moving at a non-zero constant acceleration. In this case, the distance covered does not increase linearly with time, but rather depends on the object`s initial velocity.

Option 4 states that the distance covered depends on the object`s initial displacement. While the initial displacement can influence the distance traveled by the object, it is not the primary factor. The object`s initial velocity and constant acceleration play a more significant role in determining the distance covered.

Therefore, the correct answer is Option 1, which correctly states that the distance an object covers in a certain interval of time depends on its initial velocity.