угол поворота тела вокруг оси изменяется по закону фи(t) = 0,1t2-0,5t+0,2. Найти угловую скорость вращения тела в момент времени t=20с

To find the angular velocity of the body at t = 20s, we need to differentiate the angle of rotation function φ(t) with respect to time.

Given: φ(t) = 0.1t^2 - 0.5t + 0.2

To differentiate this function, we can use the power rule for differentiation:

dφ(t)/dt = d/dt (0.1t^2 - 0.5t + 0.2) = 0.2t - 0.5

Substituting t = 20s into the derived expression, we have:

dφ(t)/dt = 0.2 * 20 - 0.5 = 4 - 0.5 = 3.5 rad/s

Therefore, the angular velocity of the body at t = 20s is 3.5 rad/s.