How to find angular acceleration - 02

The angular displacement of a particle is given by

𝜃= 〖5𝑡〗^3+〖10𝑡〗^2−2𝑡+3, where time ‘t’ is in second and 𝜃 is in rad. The angular acceleration of particle at

t = 3 sec

a) 90 𝑟𝑎𝑑 𝑠^(−2)                     b) 110 𝑟𝑎𝑑 𝑠^(−2) 

c) 100 𝑟𝑎𝑑 𝑠^(−2)                   d) 120 𝑟𝑎𝑑 𝑠^(−2)

𝜃=〖5𝑡〗^3+〖10𝑡〗^2−2𝑡+3

w. k .t. Angular velocity is time  rate of change of angular displacement.

𝜔=𝑑𝜃/𝑑𝑡=  𝑑/𝑑𝑡  (〖5𝑡〗^3+〖10𝑡〗^2−2𝑡+3)

𝜔=〖15𝑡〗^2+20𝑡−3

Also,

An acceleration is time rate of change of angular velocity

𝛼=𝑑𝜔/𝑑𝑡=𝑑/𝑑𝑡(〖15𝑡〗^2+20𝑡−3)

𝛼=30𝑡+20−0

At time t=3 second, the angular acceleration is

𝛼=30(3)+20

𝛼=90+20

𝛼=110 𝑟𝑎𝑑 𝑠^(−2)