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Finding constant acceleration, unit difficulty

  1. May 17, 2015 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    final velocity = initial velocity + (acceleration x time)

    3. The attempt at a solution
    36m/s = 4m/s + a(4s)
    32m/s = a(4s)
    a = 8?

    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 cancelled 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.
  2. jcsd
  3. May 17, 2015 #2


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    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.
  4. May 17, 2015 #3
    Thank you so much, I knew I was making an elementary mistake. I'm an idiot.
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