Question

I need help with this problem...

Answer 1

they have asked angular distance and not angular displacement!
and we know \[\theta = \omega . t\]
so when we see the graph given: \[\omega \rightarrow t\]
the area under the curve gives the Angular distance covered! For \[\omega \] to be positive it's fine, but sometimes we make a mistake by subtracting that area which is under X axis where angular velocity is negative, but we know that distance and angular distance are not vectors and do not depend on direction of motion so we will take that area also positive here!

Answer 2

So how do I get the answer?

Answer 3

The area under the graph represents the distance travelled.

(rangaran's point above is that some of the travel is in one direction, and some in the reverse direction. The question does not ask for the resultant - but the total radians covered) This means that the total area between the line and th eX axis is to be calculated.

The area is made up of a series of triangles and rectangles.

Just get the area of each triangle or rectangle and add them all together to get the total angular distance travelled

Answer 4

CORRECTION
I didn't read the question fully:

It asks for the travel in the first 8 minutes - this is the area ABOVE the X axis only.

The method is the same

Answer 5

I got 50, thanks!