Question

An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 0.3 rad, b = 0.85 rad/s2 and c = 0.035 rad/s3

Answer 1

I found a missing question online. What is the magnitude of the angular displacement of the ride in radians between times t=0 and t= t1?
We can imagine our ride traveling from the starting point A to some point B (at t=1s).
We can find the angle of both points, and when we subtract them we get angular displacement.
$A: \theta(0)=a\\ B: \theta(1)=a+b(1)^2-c(1)^3=a+b-c$
Our angular displacement is:
$\Delta\theta=\theta(1)-\theta(0)=a+b-c-a=b-c=0.85-0.035=0.815 rad$