Unit 5: Calculus
Topic 5.9: Kinematics Questions
Practice 8 exam-style questions for IB Math AA SL Topic 5.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026• Aimnova practice — 5.9.1
A particle moves with displacement s = 2t³ − 9t² + 12t metres. Find its velocity and acceleration.
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2026• Aimnova practice — 5.9.1
A particle has velocity v = t² − 5t + 6 m/s. Find the times when it is at rest.
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2026• Aimnova practice — 5.9.1
A ball is thrown up with height h = 20t − 5t² metres. Find its velocity, the time it reaches maximum height, and that height.
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2026• Aimnova practice — 5.9.1
A particle has acceleration a = 4t − 6 m/s² and velocity 5 m/s when t = 0. Find v(t).
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2026• Aimnova practice — 5.9.1
A particle has velocity v = 18 + 6t − 3t² m/s. Find its maximum velocity.
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2026• Aimnova practice — 5.9.1
A particle has velocity v = 3t² − 12t + 9 m/s (s = t³ − 6t² + 9t). Find the displacement and the total distance travelled from t = 0 to t = 2.
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2026• Aimnova practice — 5.9.1
A particle's velocity is v = 5t·e−t m/s for t ≥ 0. Find the time at which the velocity is greatest, to 3 s.f.
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2026• Aimnova practice — 5.9.1
A particle's velocity is v = t² − 6t + 8 m/s. Find the total distance travelled from t = 0 to t = 4.
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