- #1
Square1
- 143
- 1
The concept of a "rate"
Here's another question from good ol square :|
I was hoping to get some clarification about the concept of a rate of two quantities, with different units, like speed [itex]\frac{a-units}{b-units}[/itex]. How does the expression for division [itex]\frac{a-units}{b-units}[/itex] arise from the statement like 'a' meters per 'b' seconds?
If I were to plot meters vs. time for some object moving at constant speed, I can get the 'rate' of the curve by using the definition of slope like we were taught Δmeters/Δtime ie the speed.
I also understand that acceleration is the change in velocity, 'per' given desired time interval ie Δvelocity/Δtime.
In both cases, I don't think I have conceptual issue with why it makes sense to define these rates of change with respect to time, I just don't understand what division has to do with it - multiple subtractions of units of time, from the numerator?? :S Thanks.
Here's another question from good ol square :|
I was hoping to get some clarification about the concept of a rate of two quantities, with different units, like speed [itex]\frac{a-units}{b-units}[/itex]. How does the expression for division [itex]\frac{a-units}{b-units}[/itex] arise from the statement like 'a' meters per 'b' seconds?
If I were to plot meters vs. time for some object moving at constant speed, I can get the 'rate' of the curve by using the definition of slope like we were taught Δmeters/Δtime ie the speed.
I also understand that acceleration is the change in velocity, 'per' given desired time interval ie Δvelocity/Δtime.
In both cases, I don't think I have conceptual issue with why it makes sense to define these rates of change with respect to time, I just don't understand what division has to do with it - multiple subtractions of units of time, from the numerator?? :S Thanks.