Final answer:
To find the position, velocity, and acceleration vectors of a particle moving along a circular path with a given position as a function of time, we can use trigonometry and calculus.
Step-by-step explanation:
To find the position, velocity, and acceleration vectors of a particle moving along a circular path, we can use trigonometry and calculus. Given that the position as a function of time is given by θ=cos2t, where θ is in radians and t is in seconds, we can find the angular velocity by taking the derivative of θ with respect to time. The angular velocity is then 2 times the derivative of cos2t, which is -4sin2t.
The velocity vector is then found as the product of the angular velocity and the radius of the circular path. In this case, the radius is 4 in., so the velocity vector is -4sin2t times 4 in., or -16sin2t in. The acceleration vector can be found by taking the derivative of the velocity vector with respect to time. The derivative of -16sin2t is -32cos2t, so the acceleration vector is -32cos2t in.
Summary:
The position vector is θ=cos2t. The velocity vector is -16sin2t in. The acceleration vector is -32cos2t in.