Free Kinematics questions for IGCSE Additional Mathematics (0606), part of Vectors & calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Kinematics worksheet →All Vectors & calculus questionsA particle moves so that its displacement from O after t seconds is s = 2e−t + 2t m.
Find the velocity and the acceleration when t = ln 2, and explain whether the particle is speeding up or slowing down at this time.
| Part | Answer and marking points | Marks |
|---|---|---|
| v = 1; a = 1 v = −2e−t + 2 M1 v = 1 m/s A1 a = 2e−t = 1 m/s² A1 speeding up (v and a same sign) B1 | 4 |
A particle moves in a straight line. Its displacement, s m, from O after t s is s = 2t3 − 18t2 + 48t.
Find the times when the particle is instantaneously at rest.
Find the acceleration when t = 5.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | t = 2 and t = 4 v = dsdt M1 v = 0 solved M1 t = 2, 4 A1 | 3 |
| (b) | 24 m s−2 a = dvdt = 12t − 36 M1 24 A1 | 2 |
A particle moves in a straight line so that its velocity t seconds after passing a fixed point O is v = 6t2 − 24t m/s.
Find the acceleration when t = 1.
Find the time when the particle is instantaneously at rest (t > 0).
Find the displacement from O when t = 12.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −12 m/s² differentiate M1 −12 A1 | 2 |
| (b) | t = 4 v = 0 M1 t = 4 A1 | 2 |
| (c) | 1728 m s = 2t3 − 12t2 M1 1728 m A1 | 2 |
A particle moves so that its displacement from O after t seconds is s = 4e−t + 4t m.
Find the velocity and the acceleration when t = ln 2, and explain whether the particle is speeding up or slowing down at this time.
| Part | Answer and marking points | Marks |
|---|---|---|
| v = 2; a = 2 v = −4e−t + 4 M1 v = 2 m/s A1 a = 4e−t = 2 m/s² A1 speeding up (v and a same sign) B1 | 4 |
A particle moves in a straight line. Its displacement, s m, from O after t s is s = 2t3 − 21t2 + 60t.
Find the times when the particle is instantaneously at rest.
Find the acceleration when t = 6.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | t = 2 and t = 5 v = dsdt M1 v = 0 solved M1 t = 2, 5 A1 | 3 |
| (b) | 30 m s−2 a = dvdt = 12t − 42 M1 30 A1 | 2 |
A particle moves in a straight line so that its velocity t seconds after passing a fixed point O is v = 9t2 − 30t m/s.
Find the acceleration when t = 1.
Find the time when the particle is instantaneously at rest (t > 0).
Find the displacement from O when t = 10.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −12 m/s² differentiate M1 −12 A1 | 2 |
| (b) | t = 103 v = 0 M1 t = 103 A1 | 2 |
| (c) | 1500 m s = 3t3 − 15t2 M1 1500 m A1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in