Unit 5: Calculus
Topic 5.9: Kinematics Questions
Practice 20 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.
1Find2 marks
2026
A particle has velocity v = t2 − 5t + 6 m/s. Find the times when it is at rest.
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2026
Write down an expression for its acceleration.
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2026
The displacement of a particle is , where is a constant. Show that its acceleration satisfies .
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2025
A skydiver's velocity is m s. Write down the value that her velocity approaches as increases.
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2026
The velocity, v m s−1, of a particle at time t seconds is given by v = (t2 − 9)e0.3t + 4, for t ≥ 0.
Find the initial velocity of the particle.
Find the initial velocity of the particle.
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2025
A particle has velocity m s. Write down its initial velocity.
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2026
Show that the particle starts from rest.
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2024
A particle has velocity m s. Find its velocity when .
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2025
Two cyclists ride along a straight road. For t ≥ 0 seconds their velocities, in m s−1, are vP = 25 − 2t2 and vQ = 6 + 4 sin t.
Write down the initial speed of
(i) cyclist P;
(ii) cyclist Q.
Write down the initial speed of
(i) cyclist P;
(ii) cyclist Q.
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2025
A boat and a jet ski move along the same straight line. For t ≥ 0 seconds their velocities, in m s−1, are vboat = 40e−0.2t and vjet = 3t.
When t = 0, write down the speed of
(i) the boat;
(ii) the jet ski.
When t = 0, write down the speed of
(i) the boat;
(ii) the jet ski.
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2025
A particle has displacement s(t) = 3e−0.5t sin(πt/2) cm from O at time t seconds, t ≥ 0. The first time after t = 0 that the particle passes through O is t = T.
Write down the value of T.
Write down the value of T.
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2026
A particle moves with displacement metres. Find its velocity and acceleration.
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2026
A particle moves with displacement s = 2t3 − 9t2 + 12t metres. Find its velocity and acceleration.
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A particle has displacement s(t) = 4e−0.3t sin(πt/3) cm from O at time t seconds, t ≥ 0. The first time after t = 0 that the particle passes through O is t = T.
Write down the value of T.
Write down the value of T.
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2025
The displacement of a particle from is cm, . Write down the first time at which it is back at .
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2026
A particle has velocity . Find the times when it is at rest.
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2026
Sketch the velocity-time graph, showing when the particle is at rest and when it moves backwards.
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2026
A particle has acceleration a = 4t − 6 m/s2 and velocity 5 m/s when t = 0. Find v(t).
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A particle has acceleration and velocity when . Find .
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2026
A particle has velocity . Find its maximum velocity.
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