course Phy 231 A ball starting from rest rolls 13 cm down an incline on which its acceleration is 27 cm/s2, then onto a second incline 39 cm long on which its acceleration is 13 cm/s2. How much time does it spend on each incline? Answer: First ramp: v0=0cm/s, ds =13cm, vf^2 = v0^2 +2ads = 2(27cm/s^2)(13cm) = 702cm^2/s^2, vf=26.5cm/s, dv=26.5cm/s, dt=acc/dv = 27cm/s^2 / 26.5cm/s = 1.02s. Second ramp: v0=26.5cm/s, ds=39cm, vf^2=v0^2 +2ads=702cm^2/s^2 + 2(13cm/s^2)(39cm) = 1716cm^2/s^2, vf=41.4, dv =41.4cm/s-26.5cm/s = 14.9cm/s. dt=acc/dv = 13cm/s^2 / 14.9cm/s = .87s.