Question

When an electric motor is turned on at t = 0, its angular acceleration is 𝛼 = 10e-0.5t where t is the time in seconds. What is the terminal angular velocity of the motor in rpm?

Answer 1

$\alpha = 10 e^{-0.5t}= 10e^{-\frac{t}{2}}\\ \alpha = \frac{dw}{dt} =10e^{-\frac{t}{2}}\\ \int\alpha = \int\frac{dw}{dt} =\int10e^{-\frac{t}{2}}\\ \int _0^w dw =\int_{t=0} ^{t=\infin } 10e^{-\frac{t}{2}} dt\\ w =\frac{10e^{-\frac{t}{2}}}{-\frac{t}{2}} dt\\ w=-20e^{-\frac{t}{2}}|_0^{\infin}\\ w=20 rad/sec =190.985932 RPM$