On a velocity-time graph, what is the progression of motion as the line transitions from horizontal to a positively curved line to a negatively curved line?

• A. Deceleration, constant velocity, acceleration
• B. Constant velocity, acceleration, deceleration
• C. Acceleration, constant velocity, deceleration
• D. Constant velocity, deceleration, acceleration

Answer: (B)

On a velocity-time graph, the slope represents acceleration. A horizontal line means velocity isn’t changing, so there is no acceleration. When the line curves upward (positive curvature), the slope becomes steeper in the positive direction, so acceleration is positive and increasing—the object is speeding up. If the line then curves downward (negative curvature), the slope decreases and can become negative, meaning acceleration has switched to negative and the velocity begins to decrease. This sequence—constant velocity, speeding up, then slowing down—maps to constant velocity, acceleration, deceleration.