Particle system to delay start

how do I make a particle system to start when another particle system collides with ground
or at a certain second from its start ?

If you want particle system to start after certain time period from an event, you can do

int TRIGGER_TIME = 20;

//increase the timer per frame
update()
{
  timer++;

  if(timer > TRIGGER_TIME && !emitter.emit)
    emitter.emit = true
}

// Initialize the timer when the event occurs
onWhateverEvent()
{
  timer= 0;
}

if you want emitter to slowly increase emitting the particles, 
play around with emitter.maxEnergy

int MAX_ENERGY = 5;

// in update do
if(emitter.maxEnergy < MAXENERGY)
  emitter.maxEnergy += 0.01f;

Hope it helps !!