OK folks, here's a little time-waster that I got sucked into, but interestingly, I came to the same conclusion — that the units for acceleration are wrong — but by a different road. Richard was right at the very outset of this discussion — acceleration is not velocity squared — it's the delta velocity over the delta time. But I never really understood a = d/t², so I sat down and worked through it. My conclusion is that t² is incorrect, because the subscripts have been dropped.

 

Acceleration

a	=	Δv/Δt
	=	((d1/t1) − (d2/t2)) / (t1 − t2)
	=	(d3/t3) / t4
	=	d3 / (t3 × t4)
where:
a	=	acceleration
Δ	=	difference
v	=	Velocity
d	=	distance
t	=	time

1. Acceleration is the delta velocity divided by the delta time.
2. Finding the difference between two velocities is easy enough.
3. This yields a new d/t, with new subscripts to distinguish them.
4. In the last line, t₃ doesn't necessarily equal t₄, so it's incorrect to call it t².

So d/t² is a cryptic short-hand for how we're actually calculating acceleration. No problem unless we go substituting this into other equations, forgetting that it's a synthetic unit.

 

I feel so much better now.