Yes, if an object's velocity is increasing, its displacement will also increase over time. Displacement refers to the change in position of an object from its initial position to its final position.
When an object's velocity increases, it means that it is covering more distance in a given amount of time. This increased distance traveled corresponds to an increase in displacement.
To illustrate this, let's consider an example. Suppose you start at a certain point and begin walking in a straight line with an initial velocity of 1 meter per second. As time progresses, your velocity increases to 2 meters per second. In the first second, you would have covered a distance of 1 meter, resulting in a displacement of 1 meter from your initial position. However, in the next second, with an increased velocity of 2 meters per second, you would cover a distance of 2 meters, resulting in an additional displacement of 2 meters. Thus, your displacement is increasing over time as your velocity increases.
It's important to note that displacement takes into account the object's change in position from the start to the end, regardless of the path taken. It is a vector quantity that considers both magnitude (distance) and direction, while distance is a scalar quantity that refers to the total length covered without considering direction.