Randall D. Knight — Dynamics II: Motion in a Plane: Problem 60

Scientists design a new particle accelerator in which protons (mass \( 1.7 \times 10^{-27} \text{ kg} \)) follow a circular trajectory given by \( \vec{r} = c \cos(kt^2) \hat{i} + c \sin(kt^2) \hat{j} \), where \( c = 5.0 \text{ m} \) and \( k = 8.0 \times 10^4 \text{ rad/s}^2 \) are constants and \( t \) is the elapsed time. (a) What is the radius of the circle? (b) What is the proton's speed at \( t = 3.0 \text{ s} \)? (c) What is the force on the proton at \( t = 3.0 \text{ s} \)? Give your answer in component form.