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The area of an acceleration-time graph is:

The area of an acceleration-time graph is:
(1) time
(2) velocity 
(3) acceleration
(4) displacement 

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Kenneth S. | Algebra/Trig/Precalculus/Calculus Instructor Can Be Your TutorAlgebra/Trig/Precalculus/Calculus Instru...
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acceleration a(t) = v'(t) or dv/dt, rate of change of velocity.
 
Therefore the antiderivative of acceleration is velocity because ∫v'(t)dt = v(t) + C   (& C is resolved based on initial conditions).