CAIE A-Level Mathematics 4.2.2 Complex loci

CAIE A-Level Mathematics 4.2.2 Complex loci
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

  • 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

Question 2(a)

[Maximum number: 1]

An athlete runs along a straight horizontal road. The athlete starts from rest and accelerates at 0.5 ms−20.5 \mathrm{~ms}^{-2} reaching a speed of V ms−1V \mathrm{~ms}^{-1}. The athlete maintains this speed of V ms−1V \mathrm{~ms}^{-1} for T s before decelerating at 0.2 m s−20.2 \mathrm{~m} \mathrm{~s}^{-2} back to rest. The athlete covers a total distance of 1350 m in 246 seconds.

Sketch the velocity-time graph for the motion of the athlete.

Figure for Question 2(a) — CAIE A-Level Mathematics