Finding constant acceleration, unit difficulty

[PhysicallyAbel]

Homework Statement

An Indy 500 race car's velocity increases from 4m/s to 36m/s over a 4 second time interval. What is its acceleration? 4m/s is the initial velocity, 36 m/s is the final velocity, and time is 4 seconds.

Homework Equations

final velocity = initial velocity + (acceleration x time)[/B]

The Attempt at a Solution

36m/s = 4m/s + a(4s)
32m/s = a(4s)
a = 8?[/B]

Here's my problem. I know how to work out the equation and solve for acceleration. However, when you divide 32m/s by 4 seconds, I thought that you canceled the units. Which means you would be left with 8 meters (because seconds cancel out). However, I'm aware the correct answer is 8m/s^2 because acceleration is always squared.

Can someone explain my fundamental misunderstanding? It's so simple, but It's really confusing me.

 

[Orodruin]

You cannot cancel the units, both time units are in the denominator:

1 m/s / (1 s) = 1 ((m/s)/s) = 1 m/s^2

just as (1/2)/2 = 1/4 and not (1/2)/2 = 1.

 

[PhysicallyAbel]

You cannot cancel the units, both time units are in the denominator:

1 m/s / (1 s) = 1 ((m/s)/s) = 1 m/s^2

just as (1/2)/2 = 1/4 and not (1/2)/2 = 1.

Thank you so much, I knew I was making an elementary mistake. I'm an idiot.