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Antiderivative of Velocity
If a particle moves along the yaxis with continuous velocity v = f(t), the position y = F(t) is an antiderivative of the velocity, because v = dy/dt. The Fundamental Theorem of Calculus shows that the distance moved (the change in y) between times t=a and t=b is equal to the definite integral of the velocity, distance moved = F(b)  F(a) = A particle moves along the yaxis with velocity v = 8t^{3} cm/sec. How far does it move between times f = 1 and t = 2 sec? The function G(t) = 2t^{4} is an antiderivative of the velocity v = 8t^{3}. Thus the definite integral is distance moved == 30 cm.


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