EDIT: This is not a power that requires cleverness.
Pretty much. Easy ways to kill people range from the simple:
Accelerate the rock from your hand to a high speed towards the target, bullet style.
to the direct approach:
Accelerate your target downwards into the ground they are standing on extremely quickly.
to the cruel:
Give their lower body a .01 inch/s constant acceleration downwards and their upper body a .01 inch/s constant acceleration upwards.
to the extreme:
Give every molecule in their body a high acceleration out away from every other molecule
to the overkill:
Accelerate the moon towards their position rapidly.
To wit, so far this thread has thought of pretty much only one way to kill someone that doesn't involve the manipulation of acceleration through some means, so that means that it's very likely that almost every other form of killing someone can be accomplished through the manipulation of acceleration (basing off of Bay12's reliable ability to determine total forms of death and violence).
If your only ability is to accelerate your punch towards someone it's a fairly weak power since once you reach a certain point you are either going to A) Mangle your fist on impact or B) rip your fist off of your own arm. There aren't really any powerful applications that don't result in one of those two things happening. (I mean sure you could turn your fist into a one-use world-cracking bomb with that power, but you certainly wouldn't be left standing afterwards).