Trying To Calculate (Time To Top Speed)

I have 3 numbers:

1) Current Speed
2) Current Acceleration
3) Acceleration Growth

Assuming:
Current Speed=0
Current Acceleration = 0.2 (each 'turn' the current speed will increase by this much)
Acceleration Growth = 0.2 (each 'turn', the current acceleration will grow by this much)

This gives a current speed over a series of 'turns' as
0.0 + 0.2 = 0.2
0.2 + 0.4 = 0.6
0.6 + 0.8 = 1.4
1.4 + 1.0 = 2.4
2.4 + 1.2 = 3.6
3.6 + 1.4 = 5.0
5.0 + 1.6 = 6.6
6.6 + 1.8 = 8.4
8.4 + 2.0 = 10.4
etc.

What I'd like to do is have a formula (or some way other than calculating each step) to tell me how many turns it would take for the Current Speed to =>X (example 100)

Basically, Turns to X speed = something clever * acceleration growth * something else very clever.