Practice Flashcards
What is the position vector for constant-velocity motion?
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All Flashcards in Topic 3.12
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3.12.18 cards
What is the position vector for constant-velocity motion?
r(t) = r₀ + t·v — the start position r₀ plus the velocity v added on t times.
In r(t) = r₀ + t·v, how do you read off the velocity?
v is the vector multiplying t — the coefficient of t in each coordinate.
How do you find speed from a velocity vector?
speed = |v| = √(vₓ² + v_y²) — the length of the velocity vector (one positive number).
What's the difference between velocity and speed?
Velocity is a vector (direction + rate); speed is a single positive number, the magnitude of velocity.
Find the speed if v = (6, −8).
√(6² + (−8)²) = √100 = 10.
A particle has r(t) = (4 + 6t, 12 − 8t). Where is it at t = 2?
(4 + 12, 12 − 16) = (16, −4).
For steady motion, how far has an object travelled after time t?
Distance = speed × t (the path is a straight line, direction constant).
If a question asks 'how fast is it moving', what do you give?
The speed — a single positive number (the magnitude of the velocity vector), not a vector.
3.12.28 cards
What must be true for two objects to collide?
They must be at the SAME position at the SAME value of t — one t satisfies every coordinate of r_A(t) = r_B(t).
Why isn't 'paths crossing' the same as a collision?
Two objects can pass through the same point at different times; a collision needs the same point at the same moment.
How do you check for a collision?
Set r_A(t) = r_B(t), solve one coordinate for t, then CHECK that t in the other coordinate(s). If it fits all, they collide.
How do you find the distance between two moving objects?
d(t) = |r_B(t) − r_A(t)| = √((Δx)² + (Δy)²), the length of the displacement between them.
How do you find the closest approach?
Find the MINIMUM of d(t) — graph d(t) on the GDC and read the lowest point (x = time, y = least distance).
Why can you minimise d(t)² instead of d(t)?
d(t) is least exactly where d(t)² is least (both positive, square root is increasing), and d² has no awkward square root.
What does the minimum point of d(t) tell you?
Its x-coordinate is the time of closest approach; its y-coordinate is the least distance between the objects.
After finding the least distance, what should you do in an AI HL answer?
Interpret in context — compare it to the required safety/separation distance and state whether the rule is met.
Topic 3.12 study notes
Full notes & explanations for Vectors & kinematics (HL only)
Math AI exam skills
Paper structures, command terms & tips
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