ConceptConceptDocsDocuments

CAIE A-Level Mathematics 4.2.2 Complex loci

Practise reading and sketching motion graphs, using areas and gradients to connect displacement, velocity and acceleration.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • sketch velocity-time graphs with acceleration, constant speed and deceleration stages
  • use area under a velocity-time graph to find displacement or total distance
  • read gradients of displacement-time or velocity-time graphs as velocity or acceleration

4.2.2—Complex loci question 1

[Maximum number: 1]
Figure for Question 4.2.2—Complex loci question 1 — CAIE A-Level Mathematics AS

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.

All question bank results loaded