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Flip to reveal answersHow do you get velocity and acceleration from position s(t)?
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All 8 Flashcards — Kinematics with calculus
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Question
How do you get velocity and acceleration from position s(t)?
Answer
Differentiate: v = ds/dt (first derivative) and a = dv/dt = d²s/dt² (second derivative).
Question
How do you get velocity and position from acceleration a(t)?
Answer
Integrate: v = ∫a dt and s = ∫v dt — each integration adds a + C found from an initial condition (e.g. v(0), s(0)).
Question
What does 'instantaneously at rest' mean?
Answer
The velocity is zero: solve v = 0. The particle changes direction only where v actually changes sign.
Question
What is the difference between displacement and distance travelled?
Answer
Displacement = ∫v dt (signed net change in position); distance travelled = ∫|v| dt (total path length, always ≥ 0).
Question
How do you find total distance travelled by hand?
Answer
Find where v = 0, split the integral at those times, integrate each piece, then add the MAGNITUDES (or integrate |v| on the GDC).
Question
How do you find the greatest velocity in the interior of an interval?
Answer
Solve a = 0 (where dv/dt = 0, velocity is at a max/min), then also check the endpoints of the interval.
Question
Why does each integration in kinematics need a + C?
Answer
Integration only recovers the shape; the + C is the unknown starting value, fixed by an initial condition such as v(0) or s(0).
Question
A cyclist has v(t) = t² − 6t + 8 on 0 ≤ t ≤ 5. Displacement vs distance?
Answer
Displacement = ∫₀⁵ v dt = 20/3 ≈ 6.67 m; distance = ∫|v| dt (split at t = 2, 4) = 28/3 ≈ 9.33 m.
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Full study notes for Kinematics with calculus
Topic 5.13 hub
Kinematics (HL only)
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