Scientists design a new particle accelerator in which protons (mass 1 7 10 27 kg) follow a circular trajectory given by r c cos(kt 2 ) i c sin(kt 2 ) j, where c 5 0 m and k 8 0 10 4 rad s 2 are constants and t is the elapsed time a What is the radius of the circle b What is the protons 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

Question: Scientists design a new particle accelerator in which protons (mass 1.7 10 -27 kg) follow a circular trajectory given by r = c cos(kt

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.

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