Final answer:
A velocity vs. time graph shows speed changes over time, and a position vs. time graph shows displacement over time. A linear velocity-time graph means constant velocity, and a steep slope on a position-time graph represents faster velocity.
Step-by-step explanation:
When analyzing a velocity versus time graph, we are observing how the speed of an object changes over time. A position vs. time graph will show the object's displacement from its starting point as time progresses. If we have a linear velocity-time graph, which indicates a constant velocity, the corresponding position-time graph will be a straight line with a slope equal to the velocity. If the velocity is positive, the slope will be upward, and conversely, if the velocity is negative, the slope will be downward.
For instance, if we look at the scenario of driving to and from school, by multiplying the constant velocity by the time interval, we find the displacement for each part of the trip. A faster velocity would be represented by a steeper slope on the position vs. time graph.
Therefore, a constant velocity is represented by a linear, non-curved line on the distance-time graph. Each point on this graph represents the cumulative distance traveled up until that point in time. A car with a faster velocity would have a distance-time graph with a steeper slope compared to a slower vehicle.