The acceleration-time plot integral yields which quantity?

The acceleration-time plot integral yields which quantity?

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

Answer: (B)

The main idea is that acceleration is the rate of change of velocity with respect to time. Mathematically, a = dv/dt. To get velocity from acceleration, you integrate with respect to time: v(t) = ∫ a(t) dt + v0, where v0 is the velocity at the starting time. So the acceleration–time plot integral yields velocity (the definite integral over a time interval gives the change in velocity, Δv). The area under the curve tells you how much the velocity has changed, not the displacement or the force. Displacement comes from integrating velocity, and force is not obtained by time integration of acceleration.

The main idea is that acceleration is the rate of change of velocity with respect to time. Mathematically, a = dv/dt. To get velocity from acceleration, you integrate with respect to time: v(t) = ∫ a(t) dt + v0, where v0 is the velocity at the starting time. So the acceleration–time plot integral yields velocity (the definite integral over a time interval gives the change in velocity, Δv). The area under the curve tells you how much the velocity has changed, not the displacement or the force. Displacement comes from integrating velocity, and force is not obtained by time integration of acceleration.