The angular velocity of a process control motor is (21−12t2) rad/s, where t is in seconds.

A)At what time does the motor reverse direction?

I got 6.5s

B) Through what angle does the motor turn between t =0 s and the instant at which it reverses direction?

Can anyone do B

a. 21-12t^2=0 or t= sqrt21/12 which is not 6.5 seconds

b. rework a.

displacement=INT (21-12t^2) dt from o to T above

Actually it is 6.5 seconds... I worked it and that's what mastering chemistry said was correct also

To determine the angle turned by the motor between t = 0 s and the instant it reverses direction, we need to find the total change in angle.

The angle turned by the motor can be found by calculating the integral of the angular velocity with respect to time:

θ = ∫(ω) dt

Where ω represents the angular velocity of the motor.

Given that the angular velocity is (21 - 12t^2) rad/s, we can plug this into the integral:

θ = ∫(21 - 12t^2) dt

The integral of (21 - 12t^2) with respect to t will give us the angle turned by the motor.

Evaluating this integral will give us the answer to part B.

To find the angle through which the motor turns between t = 0 seconds and the instant at which it reverses direction, we need to integrate the angular velocity function over that time interval.

The given angular velocity function is (21 - 12t^2) rad/s.

Let's integrate this function with respect to time from t = 0 to the time when the motor reverses direction.

∫[(21 - 12t^2) dt] from 0 to t = t_reversal

To solve this integral, we need to find the antiderivative of the function (21 - 12t^2).

The antiderivative of (21 - 12t^2) with respect to t is found by performing power rule integration:

(21t - 4t^3/3) + C,

where C is a constant of integration.

Now, let's evaluate the definite integral using the limits of integration:

[(21t_reversal - 4t_reversal^3/3) + C] - [(21(0) - 4(0)^3/3) + C]

Simplifying further:

(21t_reversal - 4t_reversal^3/3) - 0 - (0) + C

Cancelling out the zeros:

(21t_reversal - 4t_reversal^3/3) + C.

Therefore, the angle through which the motor turns between t = 0 s and the instant at which it reverses direction is (21t_reversal - 4t_reversal^3/3) + C.