Free Kinematics questions for IB Mathematics: Applications & Interpretation (SL & HL), HL only, part of Calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Kinematics worksheet →All Calculus questionsA cyclist’s velocity is v(t) = 5te−0.5t m s−1, for t ≥ 0 seconds.
Find the maximum velocity and when it occurs.
Find the distance travelled in the first 4 seconds.
Find the acceleration at t = 4.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 3.68 m s−1 at t = 2.00 v′(t) = 0 (M1) t = 2.00 A1 3.68 m s−1 A1 | 3 |
| (b) | 11.9 m ∫04v dt (M1) 11.9 m A1 | 2 |
| (c) | −0.677 m s−2 v′(4) (M1) −0.677 m s−2 A1 | 2 |
A particle moves with velocity v(t) = 2t e−0.5t m s−1 for t ≥ 0.
Find the maximum velocity.
Find the distance travelled in the first 4 seconds.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 1.47 m s−1 GDC/derivative (M1) 1.47 A1 | 2 |
| (b) | 4.75 m ∫v dt (M1) 4.75 A1 | 2 |
A particle moves in a straight line with velocity v(t) = t2 − 5t + 4 m s−1, for 0 ≤ t ≤ 6.
Find the times when the particle changes direction.
Find the total distance travelled.
Find the displacement at t = 6.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | t = 1, t = 4 v(t) = 0 with a sign change (M1) t = 1, t = 4 A1 | 2 |
| (b) | 15.0 m ∫06|v|dt (M1) 15.0 m A1 | 2 |
| (c) | 6.00 m ∫06v dt (M1) 6.00 m A1 | 2 |
A cyclist’s velocity is v(t) = 5te−0.4t m s−1, for t ≥ 0 seconds.
Find the maximum velocity and when it occurs.
Find the distance travelled in the first 4 seconds.
Find the acceleration at t = 4.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 4.60 m s−1 at t = 2.50 v′(t) = 0 (M1) t = 2.50 A1 4.60 m s−1 A1 | 3 |
| (b) | 14.8 m ∫04v dt (M1) 14.8 m A1 | 2 |
| (c) | −0.606 m s−2 v′(4) (M1) −0.606 m s−2 A1 | 2 |
A particle moves with velocity v(t) = 3t e−0.5t m s−1 for t ≥ 0.
Find the maximum velocity.
Find the distance travelled in the first 4 seconds.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2.21 m s−1 GDC/derivative (M1) 2.21 A1 | 2 |
| (b) | 7.13 m ∫v dt (M1) 7.13 A1 | 2 |
A particle moves in a straight line with velocity v(t) = t2 − 6t + 8 m s−1, for 0 ≤ t ≤ 6.
Find the times when the particle changes direction.
Find the total distance travelled.
Find the displacement at t = 6.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | t = 2, t = 4 v(t) = 0 with a sign change (M1) t = 2, t = 4 A1 | 2 |
| (b) | 14.7 m ∫06|v|dt (M1) 14.7 m A1 | 2 |
| (c) | 12.0 m ∫06v dt (M1) 12.0 m A1 | 2 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in