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jaredogden
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Homework Statement
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.
Homework 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
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.
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