I'm currently studying Physics 101 and I'm kinda lost on the subject of velocity and speed

I know that the speed is a scalar quantity which only has a magnitude, and velocity is a vector quantity which has a magnitude & direction.

but what does ($v$) refers to in $KE = 1/2 mv^2$?

I suppose its speed because we don't care about the direction in kinetic energy and in work as well; however, the internet says its velocity but I don't know why.


closed as off-topic by AccidentalFourierTransform, M. Enns, Chris, Alfred Centauri, Kyle Kanos Feb 15 '18 at 11:15

  • This question does not appear to be about physics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Remember that velocity is relative to some frame of reference. So for a first thing, think about what the frame is that you are measuring the KE relative to. $\endgroup$ – zeta-band Feb 14 '18 at 18:51
  • 1
    $\begingroup$ @zeta-band And so is speed... $\endgroup$ – FGSUZ Feb 14 '18 at 19:00
  • 6
    $\begingroup$ I'm voting to close this question as off-topic because it shows insufficient prior research. $\endgroup$ – AccidentalFourierTransform Feb 14 '18 at 19:11
  • $\begingroup$ @AccidentalFourierTransform Ok, good luck $\endgroup$ – Yushi Feb 14 '18 at 19:14
  • $\begingroup$ "however, the internet says its velocity" - voting to close. $\endgroup$ – Alfred Centauri Feb 15 '18 at 3:31


Let velocity be $\vec{v}$. Speed is $|\vec{v}|$. The term in KE is


  • 1
    $\begingroup$ This does demonstrate a tendency which frustrated me in classes, to use "v" to describe a speed, rather than "s." As this answer shows, it's not that they used a "v" to describe a speed, so much as they got lazy drawing the || for the magnitude of the velocity vector! $\endgroup$ – Cort Ammon Feb 14 '18 at 19:21
  • 1
    $\begingroup$ @CortAmmon Unfortunately for you, this tendency doesn't really go away. The notation $\vec{x}^2$ to denote a vector dotted with itself is prevalent through most of physics. $\endgroup$ – probably_someone Feb 14 '18 at 19:28
  • 4
    $\begingroup$ It's not laziness. The notation $\vec v{}^2$ (or $\boldsymbol v^2$) is perfectly unambiguous and standard. At this point inserting $|\,|$ is just pedantry. Why would you use more symbols than necessary, especially when they add literally no information? $\endgroup$ – AccidentalFourierTransform Feb 14 '18 at 19:31
  • 2
    $\begingroup$ @CortAmmon Well, $s$ is obviously used for "displacement" so it wasn't available for "speed"... $\endgroup$ – dmckee Feb 14 '18 at 19:55
  • 2
    $\begingroup$ @Alchimista Incorrect according to whom? Landau and Lifshitz definitely use this notation, for instance. $\endgroup$ – probably_someone Feb 14 '18 at 20:38

A little about the wording of the question: as per definition, the physical quantity called „velocity” is mathematically described by a real vector space-valued function $$ \vec{v} : I\subset \mathbb R\to \mathbb R^n. $$ In mathematics, vectors can be added, multiplied by scalars, but never raised to a power, be it 2,3, $\pi^e$, or any other number. Using a vector space, one can define external operations, such as an inner product $$ \langle,\rangle :\mathbb R^3\times \mathbb R^3 \to \mathbb R.$$ With help of this and help of the well-defined square function in the field of real numbers, one has: $$ \langle \vec{v},\vec{v}\rangle =: ||\vec{v}||^2,$$ where the quantity being squared is called norm (length) of the vector. The norm of the velocity vector is called (instantaneous) speed.

By flagrant abuse of mathematical notation, $||\vec{v}||^2$ is typically written as $\vec v^2$, or a little better as $|\vec v|^2$ which has led people to believe the velocity vector can be squared.

Bottom line, KE = 1/2 times mass of particle times (instantaneous) speed raised to the power of two.


Both are correct. In the formula $\frac{1}{2}mv^2$, direction does not matter, it is merely calculating the energy the object possess at that point in time, in whatever direction.


Not the answer you're looking for? Browse other questions tagged or ask your own question.