CAIE A-Level Mathematics 4.2 Straight-Line Kinematics Question Bank

CAIE A-Level Mathematics 4.2 Straight-Line Kinematics Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise one-dimensional displacement, velocity and acceleration using graphs, calculus and constant-acceleration formulae across single or linked stages of motion.

Exam points

  • distinguish distance and speed from signed displacement, velocity and acceleration
  • differentiate or integrate with respect to time and split distance at direction changes
  • select suvat equations for each constant-acceleration stage with consistent signs

Covered syllabus points

4.2.1—Complex loci4.2.2—Complex loci4.2.3—Complex loci4.2.4—Straight lines

Question 1(a)

[Maximum number: 1]

A crate is being pushed in a straight line along a horizontal surface by a force of magnitude 25 N inclined at 20∘20^{\circ} above the horizontal. The crate moves a distance of 12 m in 8 seconds with constant speed.

Find the constant speed of the crate.

Question 2

[Maximum number: 7]

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(a)

(a)

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

Figure for Question 2(a) — CAIE A-Level Mathematics
[ 1 ]

Question 2(b)

(b)

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

[ 4 ]

Question 2(c)

(c)

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

[ 2 ]

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.

[ 4 ]

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
[ 6 ]

Question 5(c)

[Maximum number: 2]

The diagram shows a particle P of mass 6 kg on a rough plane inclined at an angle of 30∘30^{\circ} to the horizontal. Two light inextensible strings are attached to P. The strings pass over small smooth pulleys, which are fixed at the ends of the plane. The non-vertical parts of the string are parallel to a line of greatest slope of the plane. Particles Q and R, of masses 5 kg and 2 kg respectively, hang vertically at the ends of the strings.

Both strings are taut, and the system is released from rest.
It is given that the tension in the string attached to Q is twice the tension in the string attached to R.

It is given that when the system is released from rest, P is at the midpoint of the plane. In the subsequent motion, R does not reach the pulley at the top of the plane, and P takes 1.5 s to reach the pulley at the bottom of the plane.

Find the total length of the plane.