Chapter 8, Problem 60EAP

Scientists design a new particle accelerator in which protons (mass 1.7 × 10-27 kg) follow a circular trajectory given by $\stackrel{\to }{r}=c\cos \left(k{t}^2\right)\hat{i}+c\sin \left(k{t}^2\right)\hat{j}$ 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 r = 3.0 s?

c. What is the force on the proton at t = 3.0 s? Give your answer in component form.