I am having trouble writing the reason for the part of the curve to cut the x axis at Emf = 0 and when reason for curve to form max and min peaks.
If it is a magnet which is drawn through a solenoid then the curve of emf against time is unlikely to be sine curve.
The emf will however start at zero when the magnet is a long way away from the solenoid.
The induced emf will then start increasing because the rate of change of flux linked with the solenoid is increasing because the magnetic field due to the magnet around the solenoid is increasing;
When inside the solenoid the rate of change of flux linked with the solenoid will decrease because now the magnetic field around the pole of the magnet which was remote from the solenoid will have more of an influence.
There will come a time when the magnet is about in the middle of the solenoid when the induced emf will be zero because the front pole is inducing an emf in one direction and the back pole is inducing an emf in the other direction.
As the magnet continues on its way through the solenoid the magnetic field around the rear pole will have more of an influence on the rate of change of flux and the direction of the emf will be reversed.
The emf will reach a maximum in the opposite direction and then eventually drop to zero.
So the emf will start at zero, increase, reach a maximum, decrease, become zero, increase in the opposite direction, reach a maximum in th opposite direction, decrease and then because zero.
This reversal of emf might be clearer if you use Lenz's law.
Suppose that a North pole is heading towards the solenoid.
The induced emf will produce an induced current which will oppose the change producing it ie the North pole coming towards it.
Therefore a North pole is induced at the end where the North pole pole is heading towards.
When the magnet is leaving the solenoid the South pole of the magnet needs to be attracted to the solenoid so now a North pole is induced at the the end of the solenoid. For this to happen the current and hence the emf must be in the opposite direction.
@MoniaReza Q: Can you please explain to me further why does the Emf induced decreases when the magnet is in the coil?
Here is a hand waving attempt to answer your question.
For simplicity rather than a solenoid I have drawn one (red) coil but the basic ideas are sound for a solenoid.
The induced emf in the coil is the rate of change of magnetic flux passing through the coil.
In very simple terms think of the magnetic flux as the number of magnetic field lines passing through the coil.
So now imagine that coil moving along and the number of field lines through the coil is increasing but passed diagram 2 at a reducing rate so that by the time diagram 4 is reached there is no change in the magnetic flux.