Further Parametric Equations (AQA A-Level Mathematics): Flashcards

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Modelling with Parametric Equations
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What do parametric equations define?

xx and yy as functions of parameter tt

What can parameter tt represent?

Time, angle, or another variable

Projectile horizontal motion equation

x(t)=v0cos⁡(θ)⋅tx(t) = v_0 \cos(\theta) \cdot t

Projectile vertical motion equation

y(t)=v0sin⁡(θ)⋅t−12gt2y(t) = v_0 \sin(\theta) \cdot t - \frac{1}{2}gt^2

Shape of projectile trajectory

Parabola

Circular motion horizontal component

x(t)=rcos⁡(ωt)x(t) = r \cos(\omega t)

Circular motion vertical component

y(t)=rsin⁡(ωt)y(t) = r \sin(\omega t)

What ω\omega represents in circular motion

Angular velocity

Ellipse horizontal component with semi-major axis aa

x(t)=acos⁡(t)x(t) = a \cos(t)

Ellipse vertical component with semi-minor axis bb

y(t)=bsin⁡(t)y(t) = b \sin(t)

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