The area under a velocity-time graph represents which physical quantity?

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

Answer: (A)

The main idea is that velocity is the rate at which position changes, so the area under a velocity–time graph represents the change in position over that time interval. Since v = dx/dt, integrating velocity with respect to time over a period gives ∆x, the displacement (the signed amount of position change). If velocity is positive, the area adds to give positive displacement; if velocity is negative, it subtracts, giving negative displacement. For constant velocity, the area is simply velocity × time, which matches a rectangle under the curve.

Momentum isn’t the area under the curve; it is mass times velocity. Acceleration isn’t the area either; it’s the rate of change of velocity. Distinguishing displacement from distance: the area gives signed displacement, whereas total distance would require integrating |v|.