What does the slope of a position-versus-time graph represent?

• A. Acceleration
• B. Velocity
• C. Displacement
• D. Jerk

Answer: (B)

The slope of a position-versus-time graph represents velocity. Since velocity is the rate at which position changes with time, the slope ds/dt gives how far the object moves per unit of time. A positive slope means moving in the positive direction, a negative slope means moving in the opposite direction, and the steeper the slope, the faster the motion. If the slope is constant, velocity is constant; if the slope changes, velocity is changing (that change is acceleration). The instantaneous slope at a single time gives the instantaneous velocity, while the slope between two points gives the average velocity over that interval. Displacement is the overall change in position, not the rate of change, and jerk is the rate of change of acceleration, not described by the slope of the position-time graph.