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CAIE A-Level Mathematics A2 4.2.2 Complex Loci Questions

Practise interpreting velocity-time graphs to find acceleration, distance, speed and turning points.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • interpret velocity-time graphs and their gradients
  • calculate distance travelled from areas under velocity-time graphs
  • find speeds, accelerations and key times from piecewise motion graphs

CAIE A-Level Mathematics A2 4.2.2 Complex Loci Questions question 1

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Figure for Question CAIE A-Level Mathematics A2 4.2.2 Complex Loci Questions question 1 — CAIE A-Level Mathematics A2

The displacement of a particle moving in a straight line is s metres at time t seconds after leaving a fixed point O. The particle starts from rest and passes through points P, Q and R, at times t=5, t=10 and t=15 respectively, and returns to O at time t=20. The distances O P, O Q and O R are 50 m , 150 m and 200 m respectively.

The diagram shows a displacement-time graph which models the motion of the particle from t=0 to t=20. The graph consists of two curved segments A B and C D and two straight line segments B C and D E.

Find the speed of the particle between t=5 and t=10.

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