Variable Acceleration - 1D (AQA A-Level Mathematics): Flashcards

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Using Calculus in 1D
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Displacement (in kinematics)

Distance from origin where direction matters

Velocity definition

Rate of change of displacement; direction matters

Speed definition

Rate of change of distance; direction doesn't matter

Velocity from displacement formula

v=dsdtv = \frac{ds}{dt}

Acceleration from velocity formula

a=dvdta = \frac{dv}{dt} or d2sdt2\frac{d^2s}{dt^2}

Particle stationary condition

When v=0v = 0

Max/min displacement condition

When v=0v = 0 or dsdt=0\frac{ds}{dt} = 0

Max/min velocity condition

When a=0a = 0 or dvdt=0\frac{dv}{dt} = 0

Integrating velocity vv gives

Displacement ss (plus constant)

At turning point, particle is

Stationary (no speed)

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