Final answer:
A linear displacement versus time graph indicates constant velocity and therefore zero acceleration. Since the slope of the velocity versus time graph represents acceleration and is constant, in this case, the conclusion is that the acceleration is zero.
option d is the correct
Step-by-step explanation:
If a plot of displacement versus time is linear, which means it forms a straight line, this indicates that the velocity is constant. Since acceleration is defined as the change in velocity over time, if velocity is constant, this means that there is no change in velocity and hence, the acceleration is zero. So, the correct answer in this case would be D. acceleration is zero.
Recalling that acceleration is the slope of a velocity versus time graph means a constant slope indicates constant acceleration, and a zero slope indicates zero acceleration. A linear displacement versus time graph means that we have a constant slope on a velocity versus time graph, and a constant velocity indicates no change in acceleration over time. Therefore, when displacement versus time is linear, the acceleration must be zero.