- During a certain period, the angular position of a rotating object is given by: = − + , where  is in radian and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the rotating object at = Sec.

The question is not complete. The complete question is :

During a certain period of time, the angular position of a rotating object is given by , where θ is in radians and t is in seconds.  Determine the angular position, angular speed, and angular acceleration of the door (a) at t = 0.00 seconds, (b) at t = 3.00 seconds.

Solution :

Given :

Displacement or angular position of the object,

∴ Angular speed is  

                                 ω = 10 + 4t

And angular acceleration is

                                              α = 4

a). At time, t = 0.00 seconds :

   Angular displacement is

                                               = 5 rad

  Angular speed is  ω = 10 + 4t

                                 ω = 10 + 4(0)

                                     = 10 rad/s

Angular acceleration is α = 4

b). At time, t = 3.00 seconds :

   Angular displacement is

                                               = 53 rad

  Angular speed is  ω = 10 + 4t

                                 ω = 10 + 4(3)

                                     = 22 rad/s

Angular acceleration is α = 4

explanation:

as the height from which the ruler was dropped increased, the speed of the ruler at ryan's hand increased.