Unit 3: Geometry and Trigonometry
Topic 3.12: Vectors & kinematics (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 3.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
Solving rA(t) = rB(t) gives t = 4 from the x-equation AND t = 4 from the y-equation. The objects:
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2026
In r(t) = r₀ + t·v, the vector r₀ represents:
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2026
Two objects are at the same point on the map at t = 2 and t = 5 respectively. Do they collide there?
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2026
A boat moves with constant velocity. Its position (km) is r(t) = (3 + 4t, −2 + 3t), with t in hours. Write down its velocity vector and find its speed.
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2026
A particle has velocity v = (−4, 3) m/s. Its speed is:
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A drone has r(t) = (1 + 2t, 3 − t). Its velocity vector is:
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The closest approach of two moving particles occurs at the value of t where d(t) is:
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For steady motion at speed 8 m/s, the distance travelled in 6 s is:
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Find the time of closest approach and the distance between them then.
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2026
A submarine's 3D position (km) is r(t) = (2 + 3t, −1 + 4t, 5 + 12t), with t in hours. Find its speed.
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2026
You want the least distance between two objects. Which is the easiest correct quantity to minimise on a GDC?
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2026
A plane has position vector r(t) = (100 − 20t, 50 + 15t) (km, t in hours). After how many hours is its x-coordinate equal to 40 km?
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2026
If two velocity vectors have the SAME magnitude but different directions, the two objects have:
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2026
Two boats have positions (km, t in hours) rA(t) = (1 + 3t, 2 + t) and rB(t) = (10 − 2t, t). Determine whether the boats collide.
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2026
Particles P and Q have positions (m, t in s) rP(t) = (2t, 6 − t) and rQ(t) = (8 − 2t, 2t). Find the time at which they collide and the point of collision.
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A particle moves so that r(t) = (−3 + 2t, 4 + 2t) m, with t in seconds. Find its speed, and find the distance it has travelled after 5 s.
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A drone starts at (1, 6) m and has constant velocity (5, −12) m/s. Find (a) its position after 3 s, (b) its speed.
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2026
Two cars have velocities u = (6, 8) km/h and w = (−9, 12) km/h. Which car is faster, and by how much?
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Find its velocity, its speed, and its position after seconds.
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A closest-approach calculation gives a minimum distance of 3.2 km, and the safety rule is 'stay at least 4 km apart'. The correct conclusion is:
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