A particle moves on a circle of radius R and its speed varies with angular position as v = v₀eᵏθ. The ratio aₜ/ $a_c$ is:
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A particle moves on a circle of radius R and its speed varies with angular position as v = v₀eᵏθ. The ratio aₜ/a_c is:

G1 Physics · Accepted Answer

Since s=Rθ, aₜ=v(dv/ds)=(v/R)(dv/dθ). Given v=v₀eᵏθ, dv/dθ=kv. Thus aₜ=kv²/R. Radial acceleration a_c=v²/R. Hence aₜ/a_c=k.