A particle has an acceleration of +6.24 m/s2 for 0.440 s. At the end of this time the particle's velocity is +9.36 m/s.

What was the particle's initial velocity?

a = dv/dt = 6.24

so
v = constant + 6.24 t
at t = 0, v = Vi
so
v = Vi + 6.24 t
9.36 = Vi + 6.24 * .44