A ball starting from rest rolls 11 cm down an incline on which its acceleration is 24 cm/s2, then onto a second incline 44 cm long on which its acceleration is 12 cm/s2. How much time does it spend on each incline? First we find `dt of the first incline by using the formula `ds=v0`dt +.5a`dt^2. We know v0 is 0 because the ball starts at rest and `ds and a are given. Substituting these values gives a `dt of .9 sec. Next to find the initial velocity of the second incline we find the Vf of the first one. We can do this by knowing that the acceleration is equal to the change in velocity over the change in time. If we know the change in time to be .9 and the a to be 24 cm/s the change in velocity must have been about 21.6 cm/s. This is also the vf since the initial was 0. Now we have a v0 of the second ramp of 21.6 cm/s. We can use the ^2equation vf^2=v0^2 + 2a`ds and solve for vf which is 39 cm/s. We can calculate `dv to be 39-21.6 or about 17.4. Now we use the relationship a =`dv/`dt and solve for a `dt of about 1.45 seconds.