Final answer:
Displacement over several time intervals can indicate whether motion is accelerated. If the displacement increases over each time interval, it suggests that the motion is accelerating. The correct option is D.
Step-by-step explanation:
Displacement over several time intervals can indicate whether motion is accelerated. If the displacement increases over each time interval, it suggests that the motion is accelerating. This is because acceleration is the rate at which velocity changes, and an increase in displacement indicates an increase in velocity. Therefore, option c. 'Increasing displacement indicates acceleration' is the correct answer.
Displacement over time can indicate acceleration if the displacement increases over each time interval, suggesting that velocity, and hence acceleration, is increasing. A straight displacement versus time graph indicates zero acceleration, while a curved graph shows acceleration.
Displacement over several time intervals can indicate whether motion is accelerated depending on how the displacement changes with time. Acceleration is defined as the rate at which velocity changes, not the change in displacement directly. However, if an object's displacement is increasing over each equal time interval, this suggests that its velocity is increasing, which implies that the object is accelerating (option c: Increasing displacement indicates acceleration). Conversely, if the displacement over each time interval remains constant, this would imply a constant velocity, not acceleration (option a).
Furthermore, if a plot of displacement versus time is a straight line, it indicates uniform motion and the acceleration is zero. If the plot is a curve that gets steeper over time, this indicates increasing displacement over each interval, hence acceleration (option d).
In the case of a plot of displacement versus time being a straight line, it can be said that the acceleration is zero, because the slope of the line, which represents velocity, is constant. Any curvature in the displacement-time graph indicates acceleration (option c).