Solving Real-Life Problems Using Differential Equations (Leaving Cert Applied Maths): Flashcards

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Solving Real-Life Problems Using Differential Equations
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Acceleration definition

Rate at which velocity changes with time

When to use a=dvdta = \frac{dv}{dt}

Linking velocity and time

When to use a=vdvdsa = v\frac{dv}{ds}

Linking velocity and displacement

What is retardation?

Negative acceleration or deceleration

First equation of motion (from calculus)

v=u+atv = u + at

Second equation of motion (from calculus)

s=ut+12at2s = ut + \frac{1}{2}at^2

Third equation of motion (from calculus)

v2=u2+2asv^2 = u^2 + 2as

Power formula in mechanics

Power=TvPower = Tv (TT = tractive force, vv = velocity)

Newton's law of cooling/warming states

Rate of temp change ∝ temp difference from surroundings

Newton's law of cooling formula

dθdt=kθ\frac{d\theta}{dt} = k\theta

Calculator mode for inverse trig functions

Radian mode

In Newton's law, θ\theta represents

Temperature difference between body and surroundings

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