A particle is rotating in a circular path and at any instant its motion can be described as = 5t^4 40 - t^3 3 . The angular acceleration of the particle after 10 seconds is _______ rad/s ^2 .

Step-by-step solution

Given = 5t^4 40 - t^3 3 = t^4 8 - t^3 3 Angular velocity = d dt = 4t^3 8 - 3t^2 3 = t^3 2 - t^2 Angular acceleration = d dt = 3t^2 2 - 2t At t = 10 s, = 3(10)^2 2 - 2(10) = 150 - 20 = 130 rad/s ^2 Answer: 130