a 40 cm diameter wheel accelerates uniformly from 240 rpm to 360 rpm in 6.5s

Question

how far will a point on the edge of the wheel have traveled in this time?

Answer 1

ω = 240 rev/min= 240rev/min * 2πrad/rev * 1min/60s = 25.1 rad/s
ω = 360rev/min = 360rev/min * 2πrad/rev * 1min/60s = 37.7 rad/s
Δω =37.7-25.1 =12.6 rad/s
α = Δω/Δt = 12.6rad/s / 6.5s = 1.93 rad/s²

Θ = Θo + ωt + ½αt²

Θ = 0 + 25.1rad/s * 6.5s + ½ * 1.93rad/s² * (6.5s) = 204.2 radians

For a point at radius 20cm from the axis, the distance travelled is
s = Θ*r = 204.2 rad * 40/2 = 4084 cm ≈ 41 m