Acceleration and time delta

I'm wondering how one would calculate the velocity and displacement of accelerating game objects in a way that is aware of delta time.

Currently I have the following (this is for a bounding circle of several particle-like objects that should move at the same speed but in different directions, to optimize collision checking):

Code:

`speed *= acceleration`

attack_circle.r += (speed * delta_time)

Where speed is displacement in millisecond (initially 0.21) and acceleration is a value close to 1 (here 0.98), which gives the effect of a circle expanding rapidly at the beginning and then reaching (almost) stand-still by the end of the effect.

The problem is, it doesn't take delta-time into account when calculating the speed change, and hence, the slower the game actually runs, the further the circle expands.