hello again, 2 more questions:
1) I know that the solving equation mention above (2sin(2t)cos(2t)-1) will give values of 1/8pi and -3/8pi with the negative value excluded due to the nature of the question. However, this was done with a computer programme - how do i find the answers by hand? is it a rearrangement?
2) the final part of the question asks what is the maximum distance the object will travel? is this as simple as it sounds - i.e. for this interval t=2pi and put this into the displacement equation? or is it more involved??
The equation being solved is 2sin(2t)(cos(2t)-1) = 0.
It follows that either:
1. sin(2t) = 0 => 2t = n pi => t = npi/2 where n is an integer, or
2. cos(2t) - 1 = 0 => cos(2t) = 1 => etc.
Distance is not the same as displacement.
And I assume you mean maximum distance from the origin? Or from the starting point?
Assuming you want maximum distance from the origin, note that . You need to find the maximum value of D ......
You need to go back to your class notes and/or textbook and thoroughly review all of the mathematical knowledge this question has demanded you know.
Solutions in the domain are: .
Now you need to test their nature. The easiest way to do this is to substitute into D^2 and see which ones give the largest value of D^2.
The one you found, t = pi/2, gives the minimum value (of zero) of D^2 and therefore the minimum value (of zero) of D. I think you'll find the maximum distance from the origin is 2 .......