APFIVE In a physics experiment investigating free-fall motion, the velocity of a falling object was modeled as $$v(t)=9.8*t$$ (in m/s) over the time interval $$0 \le t \le 4$$ seconds. To calculate the object’s displacement, a student attempted to compute the definite integral of the velocity function. However, the student computed only the antiderivative of $$v(t)$$ and reported the result at the upper limit without subtracting the value at the lower limit. What is the mistake made by the student?
| t (s) | v(t) (m/s) |
|---|---|
| 0 | 0 |
| 4 | 39.2 |
They mistakenly computed the average velocity instead of computing the definite integral over the interval.
They omitted evaluating the antiderivative at the lower limit and subtracting it from the evaluation at the upper limit, thus failing to apply the Fundamental Theorem of Calculus properly.
They performed integration on the wrong function by confusing velocity and acceleration.
They used the wrong antiderivative by incorrectly applying the power rule.
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