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The speed of a motor increases from 1200 rpm to 1800 rpm in 20s. How many revolutions does it make in this period of time ?

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answer is 500.

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Detailed Solution

$ω_{1} = \frac{2 π \times 1200}{60} = 40 π; ω_{2} = \frac{2 π \times 1800}{60} = 60 π$

$α = \frac{ω_{2} - ω_{1}}{t} = \frac{60 π - 40 π}{20} = π$

$θ = ω_{1} t + \frac{1}{2} α t^{2}$

$2 π n = 40 π \times 20 + \frac{1}{2} \times π \times 20 \times 20; n = 500$

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