You must know that when using equations with physical units the units of both sides of the equation must match up. For example
Unit of pressure is
Unit of volume is
Unit of work is
When you just put the units into the equation above you find that they are equal on both sides
Which is true.
When you want to convert think about what you have to multiply by to get from 1 to the other. You should get the answer
Just like fractions with algebraic expressions the units cancel when they are at the top and bottom of the fraction
So this is the equation you are working with
The input and output for the equation is when you are converting from pm/ms2 and to cm/min2
The input you already know, find the values of the written terms.
First the value of , it is easiest to think of everything relating to meters so rewriting this with meters
Now you know that there are 100 centimeters per meter so , you know that there are 10-12 meters per picometer so
Putting those values into the equation you get . i.e there are 10-10 centimeters per picometer
Now you have the value of
Next, the time part
You need to find the value of . Time squared is confusing to think in so lets change it to Just as we looked at the pm and cm problem relating to meters it is easier to think of ms and min relating to seconds.
There are 1000 milliseconds per second so
There are 60 seconds per minute so
Put those values into the equation and you get
But you wanted to know , that is just
The equation you were trying to find the conversion factors for was
We can put these values in now.
And that is the formula you must use to convert from pm/ms2 to cm/min2