A particle moves on a circular path of radius 2 m. Its speed depends on arc length s according to v² = 4 + 8s. At s = 1 m, if aₜ = N m/s², find N.
Physics · Circular Motion · kinematics of circular motion
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Question

A particle moves on a circular path of radius 2 m. Its speed depends on arc length s according to v² = 4 + 8s. At s = 1 m, if aₜ = N m/s², find N.

G1 Physics · Accepted Answer

aₜ=v(dv/ds)=½ d(v²)/ds. Since d(v²)/ds=8, aₜ=4 m/s². Hence N=4.