On a distance-time graph, what is the correct progression as the line changes from horizontal to a positive-curved line to a negative-curved line?

• A. Constant velocity, acceleration, no motion
• B. No motion, acceleration, deceleration
• C. Deceleration, acceleration, no motion
• D. Acceleration, deceleration, constant velocity

Answer: (B)

In a distance–time graph, the slope represents velocity, and how that slope changes shows acceleration. A horizontal line means distance isn’t changing, so there’s no motion at all. If the line then becomes steeper as time progresses, the slope is increasing, which means velocity is increasing—positive acceleration or speeding up. If it later becomes less steep, the slope is decreasing, so velocity is getting smaller even though distance is still increasing; that’s deceleration. So the progression from no motion to speeding up to slowing down aligns with no motion, acceleration, and deceleration.