Scientists design a new particle accelerator in which protons (mass 1.7 × 10^-27 kg) follow a circular trajectory given by r = c cos(kt²) î + c sin(kt²) ĵ, where c = 5.0 m and k = 8.0 × 10⁴ rad/s² are constants and t is the elapsed time.
a. What is the radius of the circle?
b. What is the proton’s speed at t = 3.0 s?
c. What is the force on the proton at t = 3.0 s? Give your answer in component form.