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Homework Help: Speed and Velocity(Driving Me Crazy)

  1. Jan 28, 2012 #1
    So time and time again my professor has reinforced that speed and velocity are not the same. One is a scalar the other a vector, ect... But time and time again I will be asked to solve homework problems that ask for the speed of an object, yet the answer is velocity and using equations for velocity. Let me give you an example:

    A truck covers 37.0 m in 8.90 s while smoothly slowing down to final speed of 2.70 m/s.
    (a) Find its original speed.
    Answer: using the average Velocity equation 1/2(Vi + Vf) and the fact that the average VELOCITY is 37.0m/8.90s, we can solve the equation for initial VELOCITY! and get Vi = 5.7m/s.

    Now this does not make sense to me, first of all, if we are looking for initial speed why do we use average velocity equation. Second, if they are the same in this case, which is what I think might be happening, how do you know? The problem does not state the direction of motion in anyway. when do you then know that average velocity is the same as average speed? I just dont understand this, and I try to be very strict on the words that I see being used in the problem. When I see speed, I think one thing(distance over time) and velocity another(displacement over time). Can anyone clear this issue up for me?
  2. jcsd
  3. Jan 28, 2012 #2
    Because we need to consider the direction of velocity, the average velocity is the same as average speed when it moves in one line and doesn't change the direction.

    "the average velocity equation" that you mentioned is average speed equation. If you want to compute average velocity, you need compute on the vector of velocity.
  4. Jan 28, 2012 #3
    my book Physics for Scientist and Engineers call this, average velocity equation. Although I know of the more basic one, which is displacement over time, My book still calls this equation Vx,avg(average velocity)
  5. Jan 28, 2012 #4


    Staff: Mentor

    usually speed is the velocity vector's magnitude so once you have the velocity vector you can determine its magnitude and you'll have the speed but not always:

    Displacement vs distance is another physics gotcha:

    avg speed = (dist travelled) / (travel time)

    avg velocity = (final displacement - initial displacement ) / (travel time)

    Do you see the difference?

    If I ran in a mile race around a track and did it in 4 minutes my speed would be 15mph because my distance was 1 mile and I did it in 4 minutes.

    My average velocity would be ZERO because I ended my race where I started so the displacement vector is ZERO.
    Last edited: Jan 28, 2012
  6. Jan 29, 2012 #5
    In your original problem, you are not given a direction, therefore it is called a speed (speed is a scalar has magnitude but no direction). When you solve using the velocity equation, you need to assume direction (velocity is a vector and you need to indicate both magnitude and direction). So you can say the object was initially traveling to the right, (or east or whatever direction you choose). When you compute your ans. using the velocity equation, you need to include the assumed direction. Therefore your answer to the above problem using the velocity equation is: velocity = 5.7 m/s to the right.
    The solution to the problem is asking for a speed - so you do not need to indicate direction (which is a good thing, because you do not know the original direction). Your ans. will change from 5.7 m/s to the right (which is a vector), to 5.7 m/s. (which is a scalar, and no direction should be indicated). Does that make sense?
    Last edited: Jan 29, 2012
  7. Jan 30, 2012 #6
    Yes it now makes sense to me, took a while but i got it. Thank you!
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