1. The problem statement, all variables and given/known data An outdoor track is 420 ft. in diameter. A runner increases her speed at a constant rate from 14 to 24 ft./s over a distance of 95 ft. Determine the total acceleration of the runner 2 s after she begins to increase her speed. 2. Relevant equations Vr = dr/dt Vθ = r*dθ/dt Ar = d2θ/dt2 Aθ = r*d2θ/dt2 + 2 dr/dt*dθ/dt V = r*dθ/dt eθ A = -r*(dθ/dt)2er + r*d2θ/dteθ An = v2/ρ At = dv/dt 3. The attempt at a solution diameter = 420 ft. therefore ρ = .5*420 ft. or ρ = 210 ft. An1 = (14 ft./s)2/(210 ft.) An1 = 0.933 ft./s2 An2 = (24 ft./s)2/(210 ft.) An2 = 2.74 ft./s2 I am not sure where to go from here. I know I can't use equations from rectilinear motion since this is angular. If I could find the time it takes her to run the 95 ft. I think I could use that to find an average tangential acceleration by At = Δv/Δt. If I could also find the speed at 2 s, use An = v2/ρ and find the normal component of acceleration. Taking the magnitude of the two would give me the total acceleration and α = tan-1(An/At). I'm just not sure of the next step. I'm also not sure if that is the right approach.. Thanks for your time and any help ahead of time.