Question

At time t =0, the current to the dc motor is reversed, resulting in an angular displacement of the motor shaft given by θ = (198 rad/s)t – (24 rad/s 2 )t 2 – (2 rad/s 3 )t 3 (15 marks) a. At what time is the angular velocity of the motor shaft zero? b. Ca

Answer 1

After 3 s.

Explanation:

We are told that:

`sf(theta=198t-24t^2-2t^3)`

The angular velocity is the rate of change of `sf(theta)` so we can take the 1st derivative of this and set it to zero:

`sf(("d"theta)/(dt)=198-48t-6t^2=0)`

This is a quadratic equation which we can solve for t:

`sf(t=(48+-sqrt(2,304-4xx(-6)xx198))/(-12))`

From which the 2 roots are:

`sf(t=-12color(white)xs)`

and

`sf(t=3 color(white)(x)s)`

Ignoring the -ve root we can say that the angular velocity of the motor shaft will be zero after 3 s.

If you check the graph you can see that the function cuts the t axis at these values:

graph{y=198-48x-6x^2 [-20, 20, -50, 300]}