Florida B.E.S.T. MA.912.C.5.1
The Standard
Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions and solving applications related to motion along a line.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find a general antiderivative, then use a given value to solve for the constant of integration. They build velocity from acceleration and position from velocity. They interpret signs, units, and values in motion along a line.
What Mastery Looks Like
- Given acceleration and an initial velocity, a student can find the correct velocity function, including its constant. The student can then find position and answer motion questions with correct units.
Common Misconceptions
- Students often omit the constant of integration or use the initial value as the constant without solving. They may confuse position with total distance or treat negative velocity as negative distance.
How to Assess It
- Exit ticket: A particle has a(t) = 6t - 4, v(0) = 3, and s(0) = 2. Find v(t), s(t), and the displacement from t = 0 to t = 2.
Lesson moves
Ways to Teach It
Use a motion sensor and cart, then have students compare measured motion with position and velocity functions built from an acceleration model.
Ask students to explain why integrating the same acceleration function can produce many velocity functions and how one initial value selects the correct one.
Give groups cards showing acceleration, initial values, velocity, and position functions, then have them race to build matching sets.
Model an elevator ride with piecewise acceleration, then calculate its velocity and position at each floor using stated starting conditions.
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