Calculus in kinematics
v = ds/dt, a = dv/dt. Inversely: s = ∫v dt, v = ∫a dt.
Y13 Mechanics. When acceleration varies, use calculus rather than SUVAT. Differentiate position to get velocity; differentiate velocity to get acceleration. Reverse with integration.
Worked examples
s = t³ − 6t² + 9t: v = 3t² − 12t + 9; a = 6t − 12.
Particle at rest when v = 0: t = 1 or 3.
Initial conditions to find constants of integration.
Frequently asked questions
Distance travelled vs displacement?
Displacement: net signed change. Distance: integral of |v| (always positive).
Average velocity?
Total displacement ÷ total time. Different from average speed.