Question

Starting from rest, a fan takes four seconds to attain the maximum speed of $800\text{rpm}$ (revolutions per minute). Assuming uniform acceleration, calculate the time taken by the fan in attaining half the maximum speed.

• A. $1\text{second}$
• B. $4\text{seconds}$
• C. $1.5\text{seconds}$
• D. $2\text{seconds}$

Answer 1

The correct option is D $2\text{seconds}$

Given,
At $t=0,{\omega }_0=$ initial angular speed $=0$,
at $t=4\text{sec},\omega =800\text{rpm}$
$\alpha =$ constant (angular acceleration)
Using $\omega ={\omega }_0+\alpha t$
$800=0+\alpha \times 4$ ... $\left(1\right)$

Let $t$ be the time taken in attaining the speed of $400\text{rpm}$ which is half the maximum.
Then, $\omega ={\omega }_0+\alpha t$
$\Rightarrow 400=0+\alpha t$ ... $\left(2\right)$
From eq. $\left(1\right)$ and $\left(2\right)$
$t=2\text{seconds}$