CAIE A-Level Mathematics 4.2.4 Constant-Acceleration Motion

CAIE A-Level Mathematics 4.2.4 Constant-Acceleration Motion
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise selecting and combining suvat formulae for constant acceleration in horizontal or vertical straight-line motion, including linked particles and successive journey stages.

How this is tested

  • list known values of s, u, v, a and t before choosing an equation with one unknown
  • use a separate suvat equation for each particle or stage and link shared distances or times
  • apply a consistent positive direction and reject algebraic roots that are physically impossible

Question 2

[Maximum number: 6]

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.

Question 2(b)

(a)

Find T in terms of V, and hence show that 7 V^2-492 V+2700=0.

[ 4 ]

Question 2(c)

(b)

Find the value of V, giving a justification for your answer.

[ 2 ]