Florida B.E.S.T. MA.912.C.3.9
The Standard
Find the velocity and acceleration of a particle moving in a straight line.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a position function to calculate velocity as its first derivative and acceleration as its second derivative. They evaluate each derivative at specific times and include appropriate units.
What Mastery Looks Like
- Students correctly differentiate a position function once for velocity and twice for acceleration. They evaluate both functions at a given time and report correct units and signs.
Common Misconceptions
- Students may confuse velocity with speed and ignore the sign that shows direction. They may find acceleration from the position function instead of differentiating velocity. They also may omit units or use the original position units.
How to Assess It
- Exit ticket: Given s(t) = t³ − 6t² + 9t meters, find the velocity and acceleration at t = 2 seconds, including units.
Lesson moves
Ways to Teach It
Use a motion sensor and toy car to collect position-time data, then estimate velocity and acceleration at selected times.
Ask students to explain how the signs of velocity and acceleration describe speeding up, slowing down, and direction.
Play derivative relay: teams differentiate position cards twice, label units, and match each function to a motion description.
Analyze a car's position model to find when it stops, changes direction, speeds up, and slows down.
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Printable MA.912.C.3.9 Worksheet
A ready-to-print activity worksheet aligned to MA.912.C.3.9, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- MA.912.NSO.3.3
Solve mathematical and real-world problems involving velocity and other quantities that can be represented by vectors.
- MA.912.NSO.3.1
Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in compone...
- MA.912.C.5.1
Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from veloci...
- MA.912.C.3.2
Find an equation for the tangent line to a curve at a point and use it to make local linear approximation.
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