If an oxygen molecule is moving at 4.78x10^4 cm/sec^-1, what is its speed in miles/hr^-1?

Question

If you could tell me why the second and hour are to the negative power, that would be helpful. Ex: "sec^-1"

Thanks.

Answer 1

If you write the speed (miles per hour or centimeters per second) you would write them as either:

miles per hour = miles/hour  or miles-hr^-1

centimeters per second = cm/sec  or cm-sec^-1

If you write miles/hr^-1, then what you are really writing is miles*hours, which is wrong.

Now, one mile = 1609.344 meters = 160934.4 centimeters

one hour  = (60 min/hr)*(60 sec/min) = 3600 sec

so 1 mile/hr  = 160934.4/3600 cm/sec = 44.704 cm/sec

If your oxygen molecule is moving at 4.78x10^-4 cm/sec, then it's speed in mph is:

(4.78x10^-4)/44.704 = 1.069x10^-5 miles per hour