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

Acceleration Question -- How to label the vectors of motion...

  1. Sep 17, 2015 #1
    On a velocity-time graph, if an object is speeding up in the negative direction (let's say West), the acceleration that is calculated will be negative. To show the direction, would we put [West] or [East]? Also, if the object is slowing down in the negative direction (let's say West again), would we put [West] or [East] after calculating a positive value for acceleration. A little bit confused about this...
     
  2. jcsd
  3. Sep 17, 2015 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Strictly speaking, when we say that 'the acceleration is negative' we actually mean 'the component of acceleration in the direction I just recently mentioned points in the opposite direction to that direction'. That direction that has just been mentioned is usually the positive direction of an axis of a particular coordinate system. In your example, it's the positive direction of the x axis.

    Vectors do not have positive or negative signs. They are better thought of as a specified direction and magnitude. Signs only arise when we look at the component of a vector in a given direction. When we represent a vector as a triple of numbers, the numbers can be negative, but the numbers are not the vector. They are just a representation of it in a particular coordinate basis. If you keep this in mind you can avoid confusion.

    It is common in basic mechanics for people to talk about 'negative acceleration' but that is just a shorthand for saying the projection of the acceleration vector on the vector pointing along the positive directional axis points in the opposite direction to that axis. Or in symbols

    $$\vec{a}\cdot \vec{e}_x<0$$

    where the dot represents the vector dot product (aka inner product or scalar product) and ##\vec{e}_x## is the unit vector pointing in the positive direction of the x axis.
     
  4. Sep 17, 2015 #3
    Taking the time interval A (8-10s) for example, calculating the slope of the line gives us an acceleration of 1m/s2. The positive direction in this case is East. Since the object is slowing down in the West direction, would I be correct in saying that a= 1m/s2 [West]? If it was speeding up in the West direction, a= -1m/s2 [West]?
     
    Last edited: Sep 17, 2015
  5. Sep 17, 2015 #4
    Here is the graph.
     

    Attached Files:

  6. Sep 17, 2015 #5

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No. The slope of the line in that region is the component of the acceleration in an Easterly direction. So acceleration is ##1ms^{-2}## Easterly. It is the velocity vector that points West in that region of the graph, not the accel vector.
     
  7. Sep 17, 2015 #6
    Ok, thanks. Just to confirm, is the acceleration between 7-8 seconds -5m/s2 [East]?
     
  8. Sep 17, 2015 #7

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  9. Sep 18, 2015 #8
    The acceleration is pointing East. There is no point to put a minus there. You are using E and W to indicate direction and not plus and minus. You have to pick one convention and stay with it.
     
  10. Sep 18, 2015 #9

    jtbell

    User Avatar

    Staff: Mentor

    If I saw something like "-5 units East", I'd interpret it as equivalent to "+5 units West". One way such a thing could arise is in subtracting one vector from another:

    (5 units East) - (10 units East)
    = (-5 units East)
    = (+5 units West)
     
  11. Sep 18, 2015 #10

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In the time period to which the poster was referring (7-8 seconds) the acceleration is pointing West.
     
  12. Sep 19, 2015 #11
    You are right. Then just put the direction as West.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Acceleration Question -- How to label the vectors of motion...
  1. Is acceleration motion? (Replies: 13)

  2. Vector acceleration (Replies: 6)

Loading...