1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ds/dt and dr/dt

  1. Jul 3, 2014 #1
    This is one very basic question. But I just need to confirm if I understood it right.

    Suppose a particle moves along a curve and crosses Δs path in Δt time. Then we can say the velocity of the particle is [itex]\vec{v}[/itex] = ds/dt [itex]\hat{u}[/itex]
    Where [itex]\hat{u}[/itex] is tangent to the curve.

    Also if the same particle, as it crosses Δs, goes through a displacement Δ[itex]\vec{r}[/itex] in the same time interval Δt we say [itex]\vec{v}[/itex] = d[itex]\vec{r}[/itex]/dt

    Is the V's calculated above are same (ie equal)?

    I know the question is silly, but at present this forum is the only place for me to get help.
     
  2. jcsd
  3. Jul 3, 2014 #2

    verty

    User Avatar
    Homework Helper

    The are the same. I think I know what you are thinking, that perhaps the second one is slightly smaller because the path may be curved, but any difference between ##\Delta{s}## and ##|\Delta\vec{r}|## goes to 0 in the limit, and any angle between ##\Delta\vec{r}## and the path goes to 0 in the limit as well. So in the limit they are perfectly the same, ##d\vec{r} \over dt## is exactly the vector rate of change of position which is velocity.
     
  4. Jul 3, 2014 #3
    Thanks. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Ds/dt and dr/dt
  1. Rocket F=dp/dt (Replies: 6)

  2. F=dp/dt proof? (Replies: 15)

  3. F = m(dv/dt (Replies: 2)

  4. Problems of F = dp/dt (Replies: 6)

  5. Why is dr/dt= -V (Replies: 3)

Loading...