Vectors in kinematics — position, velocity, speed
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Flip to reveal answersWhat is the position vector for constant-velocity motion?
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All 8 Flashcards — Vectors in kinematics — position, velocity, speed
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Question
What is the position vector for constant-velocity motion?
Answer
r(t) = r₀ + t·v — the start position r₀ plus the velocity v added on t times.
Question
In r(t) = r₀ + t·v, how do you read off the velocity?
Answer
v is the vector multiplying t — the coefficient of t in each coordinate.
Question
How do you find speed from a velocity vector?
Answer
speed = |v| = √(vₓ² + v_y²) — the length of the velocity vector (one positive number).
Question
What's the difference between velocity and speed?
Answer
Velocity is a vector (direction + rate); speed is a single positive number, the magnitude of velocity.
Question
Find the speed if v = (6, −8).
Answer
√(6² + (−8)²) = √100 = 10.
Question
A particle has r(t) = (4 + 6t, 12 − 8t). Where is it at t = 2?
Answer
(4 + 12, 12 − 16) = (16, −4).
Question
For steady motion, how far has an object travelled after time t?
Answer
Distance = speed × t (the path is a straight line, direction constant).
Question
If a question asks 'how fast is it moving', what do you give?
Answer
The speed — a single positive number (the magnitude of the velocity vector), not a vector.
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Topic 3.12 hub
Vectors & kinematics (HL only)
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