Say I want to emit a particle every 1 second, but I want it to live for 5 seconds. Is that possible?
It is possible but you need to adjust explosiveness parameter here more information in documentation
So what would the math be?
0: Emit particles at regular intervals (default value).
1: Emit all particles simultaneously.
0.1 = emit 1/10 of the particles at regular intervals or 90% of the interval?
That I do not know. Official docs have still long way to go. I've look at c++ source but there is no math related to explosiveness and in shaders there is this code restart_phase*= (1.0-explosiveness)
and float restart_phase = float(gl_VertexID)/float(total_particles);
float restart_phase = float(gl_VertexID)/float(total_particles);
Sorry but I cannot deduce more.