CAIE A-Level Mathematics 4.2.3 Kinematics Using Calculus

CAIE A-Level Mathematics 4.2.3 Kinematics Using Calculus
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise differentiating displacement or velocity and integrating acceleration or velocity to connect s, v and a, using initial conditions and direction changes to find motion…

How this is tested

  • differentiate displacement s(t) to obtain v(t) and differentiate again to obtain a(t)
  • integrate a(t) or v(t), using initial motion data to determine the constant
  • solve v(t) = 0 and split displacement intervals to calculate total distance travelled

Question 4

[Maximum number: 10]

A particle P moves in a straight line. At time t s after leaving a point O on the line, the acceleration a ms−2a \mathrm{~ms}^{-2} of P is given by a=k t-3, where k is a positive constant. At time t=0, the velocity of P is 1 ms−11 \mathrm{~ms}^{-1}.

Question 4(a)

(a)

Given that P is never at instantaneous rest, show that k>4.5.

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Question 4(b)

(b)

（b）Given instead that k=2.5 ，find the total distance travelled by P in the interval 1⩽t⩽31 \leqslant t \leqslant 3 ．

Figure for Question 4(b) — CAIE A-Level Mathematics
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