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CAIE A-Level Mathematics 4.2.1 Distance, Displacement, Speed and Velocity

Practise distinguishing scalar distance and speed from signed displacement, velocity and acceleration and calculating total distance, average speed or instants of rest.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • add the magnitudes of all journey sections before dividing by total time for average speed
  • use signed velocity to determine direction while reporting speed as a non-negative magnitude
  • set v = 0 to find instantaneous rest and test whether the particle changes direction

4.2.1—Complex loci question 1

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Figure for Question 4.2.1—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 average speed of the particle during its motion.

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