(i) When the bar magnet falls through the coil, the magnetic flux linked with the coil changes, so an emf (or pd) is developed across the coil.
Initially, the rate of increase of flux increases, becomes maximum and then it decreases, becomes zero. Now, magnetic flux begins to decrease, the rate of decrease increases becomes maximum and then it decreases and when the magnet is sufficiently far on the other side, the flux becomes zero and so pd induced becomes zero.
(ii) Negative peak is longer than Positive peak because magnet moves out of coil faster than it moves into the coil, so the rate of decrease of magnetic flux is faster than the rate of increase of flux.