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

The problem was this

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 Rennie Aug 2 '16 at 5:38

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  • 1
    $\begingroup$ 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? $\endgroup$ – tfb Aug 1 '16 at 20:50
  • $\begingroup$ 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? $\endgroup$ – Charlie Smith Aug 1 '16 at 21:11
  • $\begingroup$ 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... $\endgroup$ – tfb Aug 2 '16 at 5:19

Expand on what tfb said: Instructors will (at least they should) always tell you to show your work. You did a correct job of starting to show your work, but you left off units. Treat units as just another variable in the computation, always include them as part of your work. If you are converting from feet to miles, seconds to minutes, etc, that should be shown as steps and if the units work then the odds are greatly improved that all of the work is also correct.

Without units, it looks like numbers are being randomly put into the work just to get the "correct" answer. In this case, for me, none of the answers would be correct as they do not have units. Acceleration is not 3. 3 what? If however you not only include units with your answer, but you included them every step you with see that you were still mixing minutes and seconds. Get used to treating the units in this way and you will catch many errors.

  • $\begingroup$ Fantastic! Another physics person who advocates ALWAYS using units. $\endgroup$ – David White Aug 1 '16 at 23:10
  • $\begingroup$ I learned from professors who considered work done without units to not even be worth their time to look at. Numbers without units was simply wrong. Using them correctly has the added advantage of being a sanity check on your own work. $\endgroup$ – dlb Aug 5 '16 at 17:33
  • $\begingroup$ I agree 100%. I have an engineering background, so I know that the details REALLY matter. In addition, I am currently teaching high school juniors and seniors AP physics, and it is EXTREMELY difficult to get them to understand the need for units (on every number), or the fact that dimensional analysis can spot your algebra errors substantially before you get to the final answer. In addition, when students just show me a bunch of numbers multiplied together and ask me what they are doing wrong, it is VERY difficult to diagnose their errors. $\endgroup$ – David White Aug 6 '16 at 2:23

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