A wheel whose moment of inertia is $2 kg{m}^2$  has an initial angular velocity of 50 rad/s. A constant torque of 10 Nm acts on the wheel. The time in which the wheel is accelerated to 80 rad/s is

Initial angular velocity = 50 rad/s
Final angular velocity = 80 rad/s
Torque = 10 N-m

Moment of Inertia =$2 kg{m}^2$ 
Angular acceleration  $\alpha$ is given by $\tau =\mathrm{I}\alpha$

$\alpha =\frac{\tau }{\mathrm{I}}=\frac{10}{2}=5 \mathrm{rad}/{\mathrm{s}}^2$

Hence if t is the time,

$5\mathrm{t}=80-50=30$

$\mathrm{t}=6 \mathrm{s}$