How can i make a gradient which progressively expands?

I am stuck with a design for a customer. In no way am i professional with Adobe illustrator, i have picked up everything from youtube videos however i cannot find a video to help me with this. 

I am recreating a design for a vehicle print for my customer which he had produced elsewhere but that company has closed down and said that the artwork is "corrupted" on their servers conveniently.

I have attached an image of what i am trying to achieve with the gradient. It comes out of the spray gun all together and then the colours spread across. I have used the gradient tool but it is not giving me the same effect.

Any help or ideas would be greatly appreciated!!