An object initially rotating at an angular speed of 1.6 rad/sec turns through 30 revolutions during the time it experienced an angular acceleration of 0.32 rad/s^2

a) For how much time did the acceleration last?
b) What was the final angular speed?

Help please. Use the equation and then step by step and plug the numbers into that equation

I still need help. Use the kinematic equation to find the acceleration and final angular speed. Step by step to get the answer with the numbers into the kinematic equation. Please I don't understand

a. t = 1s/1.6rad * 6.28rad/rev * 30rev = 117.75 s.

b. V = Vo + a*t = 1.6 + 0.32*117.75 = 39.28 rad/s.

To find the time for which the acceleration lasted and the final angular speed, we can use the equations of rotational motion. In this case, we'll use the equations of angular displacement, angular velocity, angular acceleration, and time.

a) To find the time, we'll use the equation:

θ = ω_i * t + (1/2) * α * t²

where θ is the angular displacement, ω_i is the initial angular velocity, α is the angular acceleration, and t is the time.

Given:
θ = 30 revolutions = 30 * 2π rad (since 1 revolution = 2π radians)
ω_i = 1.6 rad/sec
α = 0.32 rad/s²

Plugging in the values into the equation, we get:

30 * 2π = 1.6 * t + (1/2) * 0.32 * t²

Simplifying the equation, we have:

60π = 1.6t + 0.16t²

To solve this quadratic equation, we'll set it equal to zero:

0.16t² + 1.6t - 60π = 0

You can use the quadratic formula or factoring to solve for t. After finding the positive value for t, you will have the time for which the acceleration lasted.

b) To find the final angular speed, we'll use the equation:

ω_f = ω_i + α * t

Using the values given, we can now plug in the numbers:

ω_f = 1.6 + 0.32 * t

Substitute the value of t that you found in part a. This will give you the final angular speed.

Remember to convert the final answer to the appropriate units, if necessary.