Your electric drill rotates initially at 5.11 rad/s. You slide the speed control and cause the drill to undergo constant angular acceleration of 0.363 rad/s^2 for 4.13 s. What is the drill's angular displacement during that time interval?

______ rad

angle=wi*time + 1/2 alpha*time^2

To find the drill's angular displacement during the given time interval, we can use the following formula:

θ = ωi*t + (1/2)*α*t^2

Where:
θ is the angular displacement
ωi is the initial angular velocity
t is the time interval
α is the angular acceleration

Given:
ωi = 5.11 rad/s
α = 0.363 rad/s^2
t = 4.13 s

Substituting the given values into the formula:

θ = 5.11 rad/s * 4.13 s + (1/2) * 0.363 rad/s^2 * (4.13 s)^2

Simplifying the equation:

θ = 21.1043 rad + 7.690299405 rad

θ = 28.7943 rad

Therefore, the drill's angular displacement during the time interval is 28.7943 radians.