Can an object change direction without slowing down and making a complete stop Is it theoretically possible for an object or particle to change to the opposite direction without making a complete stop first?
Lets say I have a fictional hammer swing setup like this: 

I fire an electron to the hammer and the hammer smashes it back, is it possible for the electron (or any other particle or body) to change direction without slowing down and making a complete stop? If not, which law defines that?
Note: the question isn't about the hammer part but that was just the first thing that came up in my mind.
 A: No, it's not possible. An instantaneous velocity change implies an infinite acceleration. An infinite acceleration would require an infinite force. 
(Some of the comments point out that you can do a U-turn, in which case the velocity is reversed without ever being zero, but I think you are asking about straight line motion.)
A: You have to consider that velocity is a vector - magnitude and direction.  If the particle has a specific velocity and you want it to change to the negative (same magnitude, exact opposite direction) then it has to stop completely in the original direction of motion.  It can follow a curved path and never stop moving, but the velocity in the original direction of motion will have to come to zero before it starts moving back in the opposite direction.  
If it is moving in the X direction originally with velocity Vx, then it can curve through the Y (or Z) direction with velocity Vy or Vz, and never stop, but at the instant when it is traveling at right angles to the original X direction, then Vx is zero.  It's stopped in that direction.  
As for the bug on the windshield, all parts of the bug have to come to a stop before reversing direction.  They just don't all stop at the same time - which is why windshields are bad for bugs.   
A: Consider a theoretical crankshaft, con rod and piston: the crank rotates continuously and transfers rotational motion into linear motion via the con rod to the piston. Given that the crank is in continual motion how can the piston be motionless at the top and bottom of the 'stroke'?
Another means of imagining the concept of a reversal of direction without stopping is to visualise a point of light revolving around a circle as viewed from above. Now visualise that circle from the side: the point of light will be seen to travel from left to right and back again. Does it stop at each extremity?
A: I think I understand your question, where the particle is in linear motion and whether or not it can instantaneously change direction without deceleration/acceleration? I don't know the proper answer myself and can only assume that the material would have to have absolutely zero elasticity or give in the material.
The only other option I can think of is a wormhole in the path of the particle where the other end is in the same position of the $x-$axis but directs the particle to come out at the same speed but in the opposite direction. This would give a perfectly vertical line from positive velocity the same negative velocity on a velocity vs time graph.
