When an alpha particle is nearing the gold atoms nucleus, it is slowing down due to electrostatic repulsion, right? But then why is the acceleration or velocity not a minimum at that point (the point where the alpha particle reverses its direction)and why is the speed a minimum? Like isn't the resultant force on the alpha particle reducing which should cause its acceleration to be minimum?
The electrostatic repulsion force becomes larger as the particles are brought closer together. Since force is proportional to acceleration, this must mean that the acceleration is at a maximum when the particles are at their closest distance.
When something changes direction, the velocity vector changes direction. Therefore, at the point of changing directions the velocity is $0$.
Isn't that because the electrostatic force invert the sense of the acceleration vector, reducing particle's speed to a minimum at that point? So the speed will be minimum, and acceleration maximum, but oriented in the opposite direction, which makes the alpha particle to reflect.