What does the slope of a velocity-time graph represent?

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

Answer: (B)

The slope of a velocity-time graph tells you how quickly velocity changes, which is acceleration. In this graph, velocity is on the vertical axis and time is on the horizontal axis, so the slope is Δv/Δt, the definition of acceleration. A positive slope means velocity is increasing in its current direction ( speeding up ), a negative slope means velocity is decreasing ( slowing down or speeding up in the opposite direction ), and a zero slope means velocity is constant. The units come out as m/s per second (m/s²). This is different from displacement, which comes from the area under the curve, and from speed, which is simply the magnitude of velocity, not how it changes over time.