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

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Solving Real-Life Problems Using Differential Equations
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12 questions from this quiz

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Which acceleration formula links velocity and time?

a=dvdta = \frac{dv}{dt}

Which formula connects velocity changes with distance travelled?

a=vdvdsa = v\frac{dv}{ds}

What does dvds×dsdt\frac{dv}{ds} \times \frac{ds}{dt} equal in the chain rule derivation?

dvdt\frac{dv}{dt}

What does ∫1v2+100dv\int \frac{1}{v^2 + 100} dv equal?

110tan⁡−1(v10)\frac{1}{10}\tan^{-1}(\frac{v}{10})

What does retardation mean in motion problems?

Negative acceleration

For retardation v325\frac{v^3}{25}, what is the equation using a=vdvdsa = v\frac{dv}{ds}?

vdvds=−v325v\frac{dv}{ds} = -\frac{v^3}{25}

Which equation derives from integrating a=dvdta = \frac{dv}{dt} for constant aa?

v=u+atv = u + at

How does power relate to tractive force and velocity?

Power =Tv= Tv

For a 1200kg car at 1500W power, what is acceleration in terms of vv?

a=54va = \frac{5}{4v}

What is Newton's law of cooling differential equation for temperature difference θ\theta?

dθdt=kθ\frac{d\theta}{dt} = k\theta

A body at 2°C in 25°C surroundings has what initial temperature difference?

23°C

What calculator mode is needed for inverse trigonometric functions?

Radian mode

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