Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gradient, rates and ratio

  1. Jul 29, 2014 #1
    Why does "per" in 3 miles per hour mean division?
    Why are gradients and rates a ratio?
     
  2. jcsd
  3. Jul 29, 2014 #2
    The meaning of "per" is "for each" .

    Now read 3 miles "for each" hour.
    And you divide the 3 miles by one hour you will get the speed of an object.
     
  4. Jul 29, 2014 #3
    Are you not familiar with the basic equation
    y = mx + b
    where m is the slope, or rate ( and b is the intercept )

    m is the ratio of the ordinate to the abscissa for any point on the line (x,y)

    If you plot y-axis as the "miles" and x-axis as the time of hours , then the slope naturally follows as miles/hour, or in English terms miles per hour.

    Same thing for gradient - for a surface that has a slope, its elevation will increase y-amount for every x-amount distance.
     
  5. Jul 29, 2014 #4

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Two "similar triangles" have the same angles but can be different sizes.

    In each case

    Tan{Θ} = Length of opposite side/length of adjacent side

    So if interested in the angle or gradiant it makes sense to compare the ratio of the sides rather than their absolute magnitude.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Gradient, rates and ratio
  1. Poisson Ratio (Replies: 3)

  2. Amplitude Ratio (Replies: 2)

  3. Gradient of a vector (Replies: 1)

  4. Gyromagnetic ratio (Replies: 2)

  5. Gear ratios (Replies: 2)

Loading...