# Simple acceleration question [closed]

I am trying to understand what I have done wrong in a problem

starting at rest, a runner reaches a velocity of 0.15 miles per minute after 3 seconds

The way the book did it was to convert the seconds to minutes:

$a = 0.15 - 0 /(3/60)$

$a = 0.15/0.05$

$a = 3$

The way I did it was to convert the miles per minute to miles per second:

$a = (0.15/60)/3$

$a = 0.0025/3$

$a = 0.0008333333$

Multiplying it by 60 to change it into minutes leaves me with

$a = 0.05$

So clearly I have done something wrong.

I thought as long as all items were in the same units, even though they changed the time and I changed the velocity, the answer should come out the same. I feel as though I have done something really simple wrong. I just can't figure out what it is.

## closed as off-topic by Emilio Pisanty, knzhou, sammy gerbil, Gert, John RennieAug 2 '16 at 5:38

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• I'm not going to quite answer the question, but give you, I hope, a big enough clue. You have, perfectly correctly changed to use units of miles and seconds, and got the correct acceleration. In those units, what are the units of acceleration? Remember that acceleration is the rate of change of velocity. So, now, you need to convert the time units to minutes: what factor do you need to do that? – tfb Aug 1 '16 at 20:50
• ahhh my final step, the 0.00083 should have been multiplied by 60 squared, x 3600 not 60! thanks for the hint. I suppose my one remaining question is, how do you know what unit of measurement the answer should be in. is it correct to assume that whatever unit the velocity is stated in, that should be the unit the answer should be in (with the time squared!). eg. in this case the velocity was miles per minute, so the answer should always be in miles per minute per minute. and not stated in seconds like i did? – Charlie Smith Aug 1 '16 at 21:11
• I think they probably want the answer in the units they used, although you could argue that any units would be correct, especially as the question used two different units for time... – tfb Aug 2 '16 at 5:19