Q331 · Practice questionTechnology-activeComplex unfamiliar8 marks
QUESTION 331 (8 marks)
A camera slider has velocity metres per second for . Its initial position is .
![Velocity graph v(t)=2 cos(t)-exp(-t) on [0,pi], starting positive and changing to negative.](/qce-data/assets/methods-2026-MM26-ORIG-093-mobile.svg)
a)[2 marks]
Determine .
b)[2 marks]
Determine when the slider changes direction, to s.
c)[4 marks]
Determine its displacement and total distance travelled, each to m.
WORKED SOLUTION
8 marksPractice marking scheme
ANSWER
a) . b) s. c) Displacement m; distance m.
Worked solution
a) Integrate velocity to give ; gives .
b) Solve numerically: . There is one root: for , increases until , then decreases to zero, crossing 1 once; for , velocity is negative. Velocity changes from positive to negative at this root.
c) Displacement is . Distance is .
Exact answers unless rounding is specified; equivalent forms accepted.
a) Integrates correctly.
a) Uses the initial position.
b) Finds the numerical zero of velocity.
b) Establishes a direction change.
c) Calculates the displacement.
c) Splits the distance integral with correct signs.
c) Evaluates the distance.
c) Gives both rounded values with units.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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