Edexcel IGCSE Maths (4MA1) · Unit 8: Calculus

Edexcel IGCSE 4MA1 Kinematics: Exam Questions and Answers

Kinematics questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the worked example first, then try the 8 exam-style questions yourself and check your working against the mark scheme.

1 worked example
8 questions with mark schemes
Higher tier · calculator allowed
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Practise kinematics in Unit 8 →Kinematics revision notes

What this topic covers

Differentiation 6: Kinematics (s, v, a): Using differentiation for displacement, velocity and acceleration in a straight line.

Kinematics worked examples

Worked example 1: Kinematics

A particle has displacement $s = 2 t^{3} - 3 t^{2}$ metres at time $t$ seconds. Find its velocity and acceleration at $t = 3$ .

Solution

$v = \frac{d s}{d t} = 6 t^{2} - 6 t$ ; at $t = 3$ : $36$ m/s.
$a = \frac{d v}{d t} = 12 t - 6$ ; at $t = 3$ : $30$ m/s².

3 steps

Tip: Differentiate s to get v, and v to get a.

Kinematics exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · medium · 2 marks

A particle moves along a straight line. Its displacement, $s$ metres, from a fixed point O at time $t$ seconds is $s = 4 t^{3} - 2 t$ . Find the velocity of the particle when $t = 2$ .

Show the answer and mark scheme

M1 v = 12t² − 2
A1 46 m/s

Answer: 46 m/s

Question 2 · medium · 2 marks

The velocity, $v$ m/s, of a particle at time $t$ seconds is $v = 3 t^{2} + 5 t$ . Find the acceleration of the particle when $t = 4$ .

Show the answer and mark scheme

M1 a = 6t + 5
A1 29 m/s²

Answer: 29 m/s²

Question 3 · medium · 3 marks

A particle moves along a straight line so that its displacement, $s$ metres, at time $t$ seconds is $s = t^{3} - 6 t^{2} + 9 t$ . Find the times when the particle is instantaneously at rest.

Full worked solution Free, no sign-in

M1 v = 3t² − 12t + 9
M1 3(t − 1)(t − 3) = 0 or correct formula
A1 t = 1 and t = 3

Answer: $t = 1$ s and $t = 3$ s

Every question here has a full worked solution. See them all →

Question 4 · hard · 3 marks

The displacement of a particle is given by $s = 2 t^{3} - 15 t^{2} + 36 t$ , where $s$ is in metres and $t$ is in seconds. Find the acceleration of the particle when $t = 1$ .

Show the answer and mark scheme

M1 v = 6t² − 30t + 36
M1 a = 12t − 30
A1 −18 m/s²

Answer: −18 m/s²

Question 5 · hard · 4 marks

A ball is thrown vertically upwards. Its height, $s$ metres, above the ground after $t$ seconds is $s = 20 t - 5 t^{2}$ . (a) Find the velocity of the ball when $t = 1$ . (2) (b) Find the maximum height of the ball. (2)

Show the answer and mark scheme

M1 (a) v = 20 − 10t
A1 10 m/s
M1 (b) 20 − 10t = 0 ⇒ t = 2
A1 20 m

Answer: (a) 10 m/s (b) 20 m

Question 6 · hard · 3 marks

The velocity of a particle, $v$ m/s, at time $t$ seconds is $v = 2 t^{2} - 8 t + 3$ . Find the velocity of the particle at the instant when its acceleration is zero.

Show the answer and mark scheme

M1 a = 4t − 8
M1 4t − 8 = 0 ⇒ t = 2
A1 −5 m/s

Answer: −5 m/s

Question 7 · very hard · 4 marks

A particle moves along a straight line. Its displacement, $s$ metres, from a fixed point O at time $t$ seconds is $s = t^{3} - 9 t^{2} + 24 t + 2$ . Find the displacement of the particle from O at each time when it is instantaneously at rest.

Show the answer and mark scheme

M1 v = 3t² − 18t + 24
M1 3(t − 2)(t − 4) = 0
A1 t = 2 and t = 4
A1 22 m and 18 m

Answer: 22 m (t = 2) and 18 m (t = 4)

Question 8 · very hard · 4 marks

A particle moves so that its displacement, $s$ metres, at time $t$ seconds ( $t \geq 0$ ) is $s = t^{3} - 4 t^{2} + 5 t$ . Find the acceleration of the particle when its velocity is 8 m/s.

Show the answer and mark scheme

M1 v = 3t² − 8t + 5
M1 3t² − 8t − 3 = 0 ⇒ (3t + 1)(t − 3) = 0
A1 t = 3 (rejects −1/3)
A1 a = 6t − 8 = 10 m/s²

Answer: 10 m/s²

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise kinematics for the exam

Unit 8 practice: Calculus in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

Questions students ask

Which Edexcel IGCSE Maths papers test kinematics?

Either Higher tier paper, 1H or 2H, can test kinematics: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more kinematics questions?

In the IGCSE student hub: Unit 8 (Calculus) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

Practise kinematics with your progress saved

Save your answers and track your progressA free account remembers the questions you have done and brings you back to this page.

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Edexcel IGCSE 4MA1 Kinematics: Exam Questions and Answers

Try it first

What this topic covers

Kinematics worked examples

Worked example 1: Kinematics

Solution

Kinematics exam-style questions

Question 1 · medium · 2 marks

Question 2 · medium · 2 marks

Question 3 · medium · 3 marks

Full worked solution Free, no sign-in

Question 4 · hard · 3 marks

Question 5 · hard · 4 marks

Question 6 · hard · 3 marks

Question 7 · very hard · 4 marks

Question 8 · very hard · 4 marks

Revise kinematics for the exam

Questions students ask

Practise kinematics with your progress saved

More Unit 8 topics: Calculus