Final answer:
A curved line on a distance-versus-time graph indicates that the object is accelerating, while a straight horizontal line means that the object is not accelerating.
Step-by-step explanation:
In a distance-versus-time graph, a curved line indicates that the object is accelerating. Specifically, if the curve of the line is steeper, it means that the object is experiencing a greater acceleration. This is because acceleration is defined as the rate of change of velocity, and a curved line on a distance-versus-time graph signifies that the velocity is changing.
For example, if the distance-versus-time graph represents the motion of a car, a steeply curved line would indicate that the car is rapidly changing its speed, which implies acceleration. On the other hand, a straight horizontal line in the distance-versus-time graph means that the object is moving at a constant speed and therefore not accelerating.